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.

23, 29, 37, 41, 53, 61, 67, 73, 101, 103, 127, 137, 163, 181, 229, 241, 281, 353, 421, 433, 601, 617, 641, 821, 887, 1093, 1433, 1489, 1697, 1759, 1877, 2081, 2083, 2237, 2297, 2381, 2657, 2801, 2953, 3461, 3529, 3557, 3917, 4153, 4349, 4637, 4721, 4789, 5441, 5689

Offset: 1

Author

Claude H. R. Dequatre, Apr 09 2022

Keywords

• nonn
• easy

Examples

			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).
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.
		

Crossrefs

Cf. A000005, A000040, A000578.

Cf. A353284, A353285.

Programs

Mathematica

Select[Prime[Range[2, 800]], IntegerQ[Surd[Max[DivisorSigma[0, Range[# + 1, NextPrime[#] - 1]]], 3]] &] (* Amiram Eldar, Jun 10 2022 *)

PARI

forprime(p=3,2000,my(v=vector(nextprime(p+1)-p-1,k,numdiv(p+k))); if(ispower(vecmax(v),3), print1(p", ")))