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.

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

Links

Table of n, a(n) for n=1..62.

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

Cf. A000005, A000040, A246655.

Cf. A353285, A353286.

Sequence in context: A060274 A345130 A005235 * A107664 A321671 A085013

Adjacent sequences: A353281 A353282 A353283 * A353285 A353286 A353287

Keyword

nonn,easy

Author

Claude H. R. Dequatre, Apr 09 2022

Status

approved