A119740 - OEIS

A119740

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

%I #7 Jan 26 2020 11:03:32

%S 298693,346501,1841141,2192933,2861461,3106981,3375781,3435589,

%T 3437813,3865429,4597013,6191461,7016213,7074901,7637941,7918373,

%U 9196309,10216901,12798901,13747429,14100661,14171653,14770981,14779189

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

%H Amiram Eldar, <a href="/A119740/b119740.txt">Table of n, a(n) for n = 1..10000</a>

%e 298693 is a term since 298694, 298695, 298696, 298697, 298698 and 298699 all have 8 divisors:

%e {1,2,11,22,13577,27154,149347,298694}, {1,3,5,15,19913,59739,99565,298695},

%e {1,2,4,8,37337,74674,149348,298696}, {1,7,71,497,601,4207,42671,298697},

%e {1,2,3,6,49783,99566,149349,298698}, {1,19,79,199,1501,3781,15721,298699}.

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

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

%K nonn

%O 1,1

%A _Zak Seidov_, Jul 29 2006