A165320 Primes p where neither the number of divisors of p+1 nor the number of divisors of p-1 is a power of 2.

17, 19, 97, 149, 163, 197, 199, 241, 293, 307, 337, 349, 449, 491, 523, 557, 577, 739, 773, 811, 881, 883, 991, 1013, 1051, 1061, 1151, 1171, 1249, 1277, 1279, 1423, 1451, 1459, 1471, 1493, 1531, 1549, 1601, 1637, 1667, 1693, 1709, 1733, 1747, 1861, 1949

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Maple

isA000079 := proc(n) RETURN( n=1 or numtheory[factorset](n) = {2}) ; end: isA165320 := proc(n) RETURN ( isprime(n) and not isA000079(numtheory[tau](n-1)) and not isA000079(numtheory[tau](n+1)) ) ; end: for n from 1 to 10000 do if isA165320(n) then printf("%d, ", n) ; fi; od: # R. J. Mathar, Sep 18 2009

Mathematica

fQ[n_] := Union[ IntegerQ@# & /@ Log[2, DivisorSigma[0, {n - 1, n + 1}]]] == {False}; Select[ Prime@ Range@ 300, fQ@# &] (* Robert G. Wilson v, Sep 16 2009 *)
Select[Prime[Range[300]], NoneTrue[Log2[DivisorSigma[0, #+{1, -1}]], IntegerQ]&] (* Harvey P. Dale, May 03 2023 *)

Prog

(PARI) is1(k) = apply(x -> x >> valuation(x, 2), numdiv(k)) > 1;
isok(p) = isprime(p) && is1(p-1) && is1(p+1); \\ Amiram Eldar, Jun 26 2025

Crossrefs

Cf. A000005, A008328, A008329, A036537, A165318, A165319.

Sequence in context: A272478 A028489 A210242 * A132242 A162873 A174379

Adjacent sequences: A165317 A165318 A165319 * A165321 A165322 A165323

Keyword

nonn

Author

Leroy Quet, Sep 14 2009

Extensions

More terms from Robert G. Wilson v and R. J. Mathar, Sep 16 2009

Status

approved