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Search: id:A049097
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| A049097 |
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Primes p such that p+1 is square-free. |
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+0
11
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| 2, 5, 13, 29, 37, 41, 61, 73, 101, 109, 113, 137, 157, 173, 181, 193, 229, 257, 277, 281, 313, 317, 353, 373, 389, 397, 401, 409, 421, 433, 457, 461, 509, 541, 569, 601, 613, 617, 641, 653, 661, 673, 677, 709, 733, 757, 761, 769, 797, 821, 829, 853, 857, 877
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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n such that core(sigma(n))=n+1 where core(x) is the square-free part of x. - Benoit Cloitre (benoit7848c(AT)orange.fr), May 01 2002
A160696(a(n)) = 1. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 24 2009]
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EXAMPLE
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29 is included since 29+1=30=2*3*5 is free of squares, 17 is not here because 18 is divided by a square,9.
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MATHEMATICA
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lst={}; Do[p=Prime[n]; If[ !SquareFreeQ[Floor[p-1]]&&SquareFreeQ[Floor[p+1]], AppendTo[lst, p]], {n, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 20 2008]
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CROSSREFS
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Cf. A000040, A005117, A039787.
Sequence in context: A026522 A122491 A002559 this_sequence A045366 A158708 A093702
Adjacent sequences: A049094 A049095 A049096 this_sequence A049098 A049099 A049100
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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)
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