cp's OEIS Frontend

A353286 Consider the number of divisors tau(k) of every composite k between prime p >= 3 and the next prime; if the largest tau(k) is a cube, then p is in the sequence.

%I A353286 #30 Jun 11 2022 03:35:41
%S A353286 23,29,37,41,53,61,67,73,101,103,127,137,163,181,229,241,281,353,421,
%T A353286 433,601,617,641,821,887,1093,1433,1489,1697,1759,1877,2081,2083,2237,
%U A353286 2297,2381,2657,2801,2953,3461,3529,3557,3917,4153,4349,4637,4721,4789,5441,5689
%N A353286 Consider the number of divisors tau(k) of every composite k between prime p >= 3 and the next prime; if the largest tau(k) is a cube, then p is in the sequence.
%e A353286 37 is a term because up to the next prime 41, tau(38) = 4, tau(39) = 4, tau(40) = 8, thus the greatest tau is 8 and 8 is a cube (2^3).
%e A353286 47 is prime but not a term because up to the next prime 53, tau(48) = 10, tau(49) = 3, tau(50) = 6, tau(51) = 4, tau(52) = 6, thus the greatest tau is 10 and 10 is not a cube.
%t A353286 Select[Prime[Range[2, 800]], IntegerQ[Surd[Max[DivisorSigma[0, Range[# + 1, NextPrime[#] - 1]]], 3]] &] (* _Amiram Eldar_, Jun 10 2022 *)
%o A353286 (PARI) forprime(p=3,2000,my(v=vector(nextprime(p+1)-p-1,k,numdiv(p+k))); if(ispower(vecmax(v),3), print1(p", ")))
%Y A353286 Cf. A000005, A000040, A000578.
%Y A353286 Cf. A353284, A353285.
%K A353286 nonn,easy
%O A353286 1,1
%A A353286 _Claude H. R. Dequatre_, Apr 09 2022