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A119730
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Primes p such that p+1, p+2, p+3, p+4 and p+5 have equal number of divisors.
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4
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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}.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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