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.

5, 7, 31, 97, 113, 167, 193, 199, 211, 263, 269, 277, 311, 317, 373, 383, 401, 439, 461, 509, 541, 547, 569, 593, 613, 631, 677, 701, 709, 727, 743, 757, 769, 857, 907, 941, 947, 1021, 1031, 1063, 1123, 1153, 1217, 1229, 1249, 1259, 1283, 1289, 1291, 1301, 1321, 1361

Offset

1,1

Links

Table of n, a(n) for n=1..52.

Example

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).
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.

Mathematica

Select[Prime[Range[2, 220]], IntegerQ[Sqrt[Max[DivisorSigma[0, Range[# + 1, NextPrime[#] - 1]]]]] &] (* 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), 2), print1(p", ")))

Crossrefs

Cf. A000005, A000040, A000290.

Cf. A353284, A353286.

Sequence in context: A359066 A153414 A284405 * A232237 A104815 A335121

Adjacent sequences: A353282 A353283 A353284 * A353286 A353287 A353288

Keyword

nonn,easy

Author

Claude H. R. Dequatre, Apr 09 2022

Status

approved