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

Author

Raphie Frank, Oct 04 2012

Keywords

• nonn

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).

Examples

			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.
		

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

Crossrefs

Cf. A008328.

Programs

Mathematica

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

PARI

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

Extensions

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