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

Author

Claude H. R. Dequatre, Apr 09 2022

Keywords

• nonn
• easy

Examples

			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.
		

Crossrefs

Cf. A000005, A000040, A000290.

Cf. A353284, A353286.

Programs

Mathematica

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