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 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 13 02:09 EDT 2020. Contains 336441 sequences. (Running on oeis4.)