

A217442


Numbers n such that d(prime(n)  1)  n, where d(k) is the number of divisors of k.


2



1, 2, 3, 4, 6, 24, 28, 30, 32, 36, 45, 48, 56, 64, 66, 72, 76, 80, 92, 96, 102, 104, 120, 126, 128, 144, 168, 176, 180, 184, 186, 192, 200, 208, 228, 236, 240, 248, 252, 256, 270, 280, 288, 292, 304, 312, 320, 328, 336, 352, 360, 364, 376, 384, 420, 424, 426
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OFFSET

1,2


COMMENTS

For n in {1,2,3,4,6}, n = d(prime(n)1). There are no others with this property, as conjectured by Raphie Frank and proved by Charles R Greathouse IV on Physics Forums (Nov, 2010).


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000
Physics Forums, Prime Indices & the Divisors of (p'_n  1): A LatticeRelated Question , Nov 2010


EXAMPLE

d(701  1)*7 = pi(701) = 126. The 126th prime is 701 and d(701  1) = 18; 18 divides 126 (7 times), so 126 is a member of this sequence.


MATHEMATICA

Select[Range[352], Mod[#, DivisorSigma[0, Prime[#]  1]] == 0 &] (* T. D. Noe, Oct 11 2012 *)


PROG

(PARI) is(n)=n%numdiv(prime(n)1)==0 \\ Charles R Greathouse IV, Oct 09 2012


CROSSREFS

Cf. A008328.
Sequence in context: A115035 A219048 A329577 * A065199 A249156 A033179
Adjacent sequences: A217439 A217440 A217441 * A217443 A217444 A217445


KEYWORD

nonn


AUTHOR

Raphie Frank, Oct 04 2012


EXTENSIONS

a(12), a(31), a(39) from Charles R Greathouse IV, Oct 09 2012


STATUS

approved



