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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
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
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved