A217442 Numbers n such that d(prime(n) - 1) | n, where d(k) is the number of divisors of k.

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

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 Lattice-Related 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