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
Claude H. R. Dequatre, Apr 09 2022
STATUS
approved