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 A119730 Primes p such that p+1, p+2, p+3, p+4 and p+5 have equal number of divisors. 0

%I

%S 13781,19141,21493,50581,142453,152629,253013,298693,307253,346501,

%T 507781,543061,845381,1079093,1273781,1354501,1386901,1492069,1546261,

%U 1661333,1665061,1841141,2192933,2208517,2436341,2453141,2545013

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

%e 13781 is OK since 13782, 13783, 13784, 13785 and 13786 all have 8 divisors:

%e {1,2,3,6,2297,4594,6891,13782}, {1,7,11,77,179,1253,1969,13783},

%e {1,2,4,8,1723,3446,6892,13784}, {1,3,5,15,919,2757,4595,13785} and

%e {1,2,61,113,122,226,6893,13786}.

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

%t endQ[n_]:= Length[Union[DivisorSigma[0, (n + Range[5])]]]==1; Select[Prime[ Range[ 200000]],endQ] (* _Harvey P. Dale_, Jan 16 2019 *)

%Y Cf. A008329, A049234.

%K nonn

%O 1,1

%A _Zak Seidov_, Jul 29 2006

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Last modified January 19 04:09 EST 2020. Contains 331031 sequences. (Running on oeis4.)