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

1,1

Links

Table of n, a(n) for n=1..50.

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A000005, A000040, A000578.

Cf. A353284, A353285.

Sequence in context: A082943 A061754 A180066 * A101784 A101802 A363074

Adjacent sequences: A353283 A353284 A353285 * A353287 A353288 A353289

Keyword

nonn,easy

Author

Claude H. R. Dequatre, Apr 09 2022

Status

approved