A119730 Primes p such that p+1, p+2, p+3, p+4 and p+5 have equal number of divisors.

13781, 19141, 21493, 50581, 142453, 152629, 253013, 298693, 307253, 346501, 507781, 543061, 845381, 1079093, 1273781, 1354501, 1386901, 1492069, 1546261, 1661333, 1665061, 1841141, 2192933, 2208517, 2436341, 2453141, 2545013

Offset: 1

Author

Zak Seidov, Jul 29 2006

Keywords

• nonn

Examples

			13781 is a term since 13782, 13783, 13784, 13785 and 13786 all have 8 divisors:
{1,2,3,6,2297,4594,6891,13782}, {1,7,11,77,179,1253,1969,13783},
{1,2,4,8,1723,3446,6892,13784}, {1,3,5,15,919,2757,4595,13785} and
{1,2,61,113,122,226,6893,13786}.
		

Links

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

Crossrefs

Cf. A008329, A049234, A119705, A119711, A119728, A119740.

Programs

Mathematica

Select[Prime@Range[1000000],DivisorSigma[0,#+1]==DivisorSigma[0,#+2]==DivisorSigma[0,#+3]==DivisorSigma[0,#+4]==DivisorSigma[0,#+5]&]
endQ[n_]:= Length[Union[DivisorSigma[0, (n + Range[5])]]]==1; Select[Prime[ Range[ 200000]],endQ] (* Harvey P. Dale, Jan 16 2019 *)