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

1,1

Links

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

Example

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}.

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 *)

Crossrefs

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

Sequence in context: A235184 A270639 A031807 * A204839 A208487 A188102

Adjacent sequences: A119727 A119728 A119729 * A119731 A119732 A119733

Keyword

nonn

Author

Zak Seidov, Jul 29 2006

Status

approved