cp's OEIS Frontend

A353285 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 square, then p is in the sequence.

%I A353285 #34 Jun 11 2022 03:35:31
%S A353285 5,7,31,97,113,167,193,199,211,263,269,277,311,317,373,383,401,439,
%T A353285 461,509,541,547,569,593,613,631,677,701,709,727,743,757,769,857,907,
%U A353285 941,947,1021,1031,1063,1123,1153,1217,1229,1249,1259,1283,1289,1291,1301,1321,1361
%N A353285 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 square, then p is in the sequence.
%e A353285 97 is a term because up to the next prime 101, tau(98) = 6, tau(99) = 6, tau(100) = 9, thus the greatest tau is 9 and 9 is a square (3^2).
%e A353285 127 is prime but not a term because up to the next prime 131, tau(128) = 8, tau(129) = 4, tau(130) = 8, thus the greatest tau(k) is 8 and 8 is not a square.
%t A353285 Select[Prime[Range[2, 220]], IntegerQ[Sqrt[Max[DivisorSigma[0, Range[# + 1, NextPrime[#] - 1]]]]] &] (* _Amiram Eldar_, Jun 10 2022 *)
%o A353285 (PARI) forprime(p=3,2000,my(v=vector(nextprime(p+1)-p-1,k,numdiv(p+k))); if(ispower(vecmax(v),2), print1(p", ")))
%Y A353285 Cf. A000005, A000040, A000290.
%Y A353285 Cf. A353284, A353286.
%K A353285 nonn,easy
%O A353285 1,1
%A A353285 _Claude H. R. Dequatre_, Apr 09 2022