A189536 The smallest prime p such that tau(p-1) + tau(p+1) = prime(n), or 0 if no such prime exists; where tau(k) is the number of divisors of k.

0, 2, 3, 5, 17, 37, 101, 0, 401, 3137, 4357, 62501, 21317, 16901, 1008017, 15877, 1020101, 33857, 69697, 14401, 331777, 78401, 32401, 57601, 828101, 40195601, 32080897, 3326977, 876097, 476101, 199374401, 4326401, 14440001, 1299601, 33918977, 3459601, 2647719937, 145540097

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 23 2011

Keywords

• nonn

Comments

This is sequence A090482(n) for prime n.

Crossrefs

Cf. A000005, A000668, A002496, A090482, A175144 (tau(p-1)+tau(p+1)).

Programs

Mathematica

nn = 25; t = Table[-1, {nn}]; t[[1]] = 0; t[[8]] = 0; cnt = 2; p = 1; While[cnt < nn, p = NextPrime[p]; s = DivisorSigma[0, p - 1] + DivisorSigma[0, p + 1]; If[PrimeQ[s], i = PrimePi[s]; If[i <= nn && t[[i]] == -1, t[[i]] = p; cnt++]]]; t (* T. D. Noe, Apr 28 2011 *)

Extensions

a(26)-a(38) from Amiram Eldar, Jan 25 2025