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Search: id:A062799
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| A062799 |
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Inverse Moebius transform of A001221, the number of distinct prime factors of n. |
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+0
8
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| 0, 1, 1, 2, 1, 4, 1, 3, 2, 4, 1, 7, 1, 4, 4, 4, 1, 7, 1, 7, 4, 4, 1, 10, 2, 4, 3, 7, 1, 12, 1, 5, 4, 4, 4, 12, 1, 4, 4, 10, 1, 12, 1, 7, 7, 4, 1, 13, 2, 7, 4, 7, 1, 10, 4, 10, 4, 4, 1, 20, 1, 4, 7, 6, 4, 12, 1, 7, 4, 12, 1, 17, 1, 4, 7, 7, 4, 12, 1, 13, 4, 4, 1, 20, 4, 4, 4, 10, 1, 20, 4, 7, 4, 4, 4
(list; graph; listen)
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OFFSET
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1,4
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LINKS
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Psychedelic Geometry Blogspot, CURIOUS SERIES-002 [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Sep 08 2009]
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FORMULA
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a(n)=Sum{A001221[d]}, where d runs over divisors of n.
Contribution from Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Sep 08 2009: (Start)
a(s)=omega(s)*2^(omega(s)-1), if s is squarefree (A005117) where omega is A001221
a(n)<=(omega(n)*tau_2(n))-1, where tau_2(n) is A000005 and n>1 (End)
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EXAMPLE
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n = 255: divisors = {1, 3, 5, 15, 17, 51, 85, 255}, a(255) = 0+1+1+2+1+2++2+3 = 12
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MATHEMATICA
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f[n_] := Block[{d = Divisors[n], c = l = 0, k = 2}, l = Length[d]; While[k < l + 1, c = c + Length[ FactorInteger[ d[[k]] ]]; k++ ]; Return[c]]; Table[f[n], {n, 1, 100} ]
Contribution from Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Sep 08 2009: (Start)
omega[n_] := Length[FactorInteger[n]]; SetAttributes[omega, Listable]
omega[1] := 0
A062799[n_] := Plus @@ omega[Divisors[n]] (End)
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CROSSREFS
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Cf. A001221.
Sequence in context: A101261 A067614 A113901 this_sequence A063647 A077808 A021471
Adjacent sequences: A062796 A062797 A062798 this_sequence A062800 A062801 A062802
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jul 19 2001
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