A119740 Primes p such that p+1, p+2, p+3, p+4, p+5 and p+6 have equal number of divisors.

298693, 346501, 1841141, 2192933, 2861461, 3106981, 3375781, 3435589, 3437813, 3865429, 4597013, 6191461, 7016213, 7074901, 7637941, 7918373, 9196309, 10216901, 12798901, 13747429, 14100661, 14171653, 14770981, 14779189

Offset: 1

Author

Zak Seidov, Jul 29 2006

Keywords

• nonn

Examples

			298693 is a term since 298694, 298695, 298696, 298697, 298698 and 298699 all have 8 divisors:
{1,2,11,22,13577,27154,149347,298694}, {1,3,5,15,19913,59739,99565,298695},
{1,2,4,8,37337,74674,149348,298696}, {1,7,71,497,601,4207,42671,298697},
{1,2,3,6,49783,99566,149349,298698}, {1,19,79,199,1501,3781,15721,298699}.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008329, A049234, A119705, A119711, A119728, A119730.

Programs

Mathematica

Select[Prime@Range[1000000],DivisorSigma[0,#+1]==DivisorSigma[0,#+2]==DivisorSigma[0,#+3]==DivisorSigma[0,#+4]==DivisorSigma[0,#+5]==DivisorSigma[0,#+6]&]