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A353284
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 prime power, then p is in the sequence.
5
3, 5, 7, 13, 23, 29, 31, 37, 41, 53, 61, 67, 73, 97, 101, 103, 113, 127, 137, 163, 167, 181, 193, 199, 211, 229, 241, 263, 269, 277, 281, 311, 317, 353, 373, 383, 401, 421, 433, 439, 461, 509, 541, 547, 569, 593, 601, 613, 617, 631, 641, 677, 701, 709, 727, 743, 757, 769, 821, 839, 857, 887
OFFSET
1,1
EXAMPLE
13 is a term because up to the next prime 17, tau(14) = 4, tau(15) = 4, tau(16) = 5, thus the greatest tau(k) is 5 and 5 is a prime power (5^1).
23 is a term because up to the next prime 29, tau(24) = 8, tau(25) = 3, tau(26) = 4, tau(27) = 4, tau(28) = 6, thus the greatest tau(k) is 8 and 8 is a prime power (2^3).
79 is prime but not a term because up to the next prime 83, tau(80) = 10, tau(81) = 5, tau(82) = 4, thus the greatest tau(k) is 10 and 10 is not a prime power.
MATHEMATICA
Select[Prime[Range[2, 155]], PrimePowerQ[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(isprimepower(vecmax(v)), print1(p", ")))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved