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Search: id:A134865
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| A134865 |
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Numbers n meeting the following criterion: if n is a multiple of d, then it is also a multiple of the smallest number with same number of divisors as d. |
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5
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| 1, 2, 4, 6, 12, 24, 36, 48, 120, 240, 360, 720, 2520, 5040, 7560, 10080, 15120, 20160, 45360, 50400, 100800, 332640, 352800, 665280, 705600, 4324320, 8648640, 17297280, 21621600, 43243200, 13492656777600
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Note that this is not a subsequence of A002182: 100800 is in this sequence but not in A002182 - J. Lowell (jhbubby(AT)mindspring.com), Feb 22 2008
A subset of A005179. - Max Alekseyev, May 19 2008
A number n is in A134865 iff for every divisor d of n, A005179(A000005(d)) (= A140635(d)) is also a divisor of n. So the question of the finiteness of A134865 is closely related to the form of the elements of A005179. - Max Alekseyev, May 19 2008, May 20 2008
Rearrangement of this sequence, forming a subsequence of A005179, is given by A140753. Corresponding indices of elements of A005179 are given by A138394 and A140752. - Max Alekseyev (maxale(AT)gmail.com), May 26 2008
A subsequence of A007416 which is a subsequence of A025487, so every term is primally tight and even (after the first term). Thus if d is a divisor of a term, then the least integer with the same prime signature as d (=A046523(d)) is also a divisor. So only the divisors that are in A025487 need be tested. - Chandler
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FORMULA
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a(n) = A005179(A140752(n)) - Max Alekseyev (maxale(AT)gmail.com), May 26 2008
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EXAMPLE
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60 is a multiple of 30 with 8 divisors, but not of 24 (the smallest number with 8 divisors) so 60 does not qualify for this sequence
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MATHEMATICA
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a = {}; For[n = 1, n < 10000, n++, b = Divisors[n]; c = 1; For[i = 1, i < Length[b] + 1, i++, j = 1; While[Length[Divisors[j]] < Length[Divisors[b[[i]]]], j++ ]; If[ ! Mod[n, j] == 0, c = 0]]; If[c == 1, AppendTo[a, n]]]; a - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Feb 05 2008
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PROGRAM
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isA134865(n)={ n%2 & return(n==1); fordiv(n, d, bigomega(d)>1|next; nd=numdiv(d); for(k=4, d, numdiv(k)==nd | next; n%k & return; break)); 1 } - R. J. Mathar, May 17 2008
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CROSSREFS
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Cf. A000005, A005179, A007416, A134865, A138394, A140752, A140753.
Sequence in context: A166981 A137425 A141320 this_sequence A140753 A050293 A048115
Adjacent sequences: A134862 A134863 A134864 this_sequence A134866 A134867 A134868
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KEYWORD
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more,nonn
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AUTHOR
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J. Lowell (jhbubby(AT)mindspring.com), Jan 29 2008
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Feb 05 2008
More terms from J. Lowell (jhbubby(AT)mindspring.com), Feb 22 2008
a(22)-a(30) from Don Reble, May 17 2008
a(31)=13492656777600 from Ray Chandler (rayjchandler(AT)sbcglobal.net), Jun 30 2008
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