cp's OEIS Frontend

A353284 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 prime power, then p is in the sequence.

%I A353284 #34 Jun 11 2022 03:35:23
%S A353284 3,5,7,13,23,29,31,37,41,53,61,67,73,97,101,103,113,127,137,163,167,
%T A353284 181,193,199,211,229,241,263,269,277,281,311,317,353,373,383,401,421,
%U A353284 433,439,461,509,541,547,569,593,601,613,617,631,641,677,701,709,727,743,757,769,821,839,857,887
%N A353284 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 prime power, then p is in the sequence.
%e A353284 13 is a term because up to the next prime 17, tau(14) = 4, tau(15) = 4, tau(16) = 5, thus the greatest tau(k) is 5 and 5 is a prime power (5^1).
%e A353284 23 is a term because up to the next prime 29, tau(24) = 8, tau(25) = 3, tau(26) = 4, tau(27) = 4, tau(28) = 6, thus the greatest tau(k) is 8 and 8 is a prime power (2^3).
%e A353284 79 is prime but not a term because up to the next prime 83, tau(80) = 10, tau(81) = 5, tau(82) = 4, thus the greatest tau(k) is 10 and 10 is not a prime power.
%t A353284 Select[Prime[Range[2, 155]], PrimePowerQ[Max[DivisorSigma[0, Range[# + 1, NextPrime[#] - 1]]]] &] (* _Amiram Eldar_, Jun 10 2022 *)
%o A353284 (PARI) forprime(p=3,2000,my(v=vector(nextprime(p+1)-p-1,k,numdiv(p+k))); if(isprimepower(vecmax(v)), print1(p", ")))
%Y A353284 Cf. A000005, A000040, A246655.
%Y A353284 Cf. A353285, A353286.
%K A353284 nonn,easy
%O A353284 1,1
%A A353284 _Claude H. R. Dequatre_, Apr 09 2022