A165319 -id:A165319 - cp's OEIS frontend

A165318 Primes p where the number of divisors of p-1 is a power of 2.

2, 3, 7, 11, 23, 31, 41, 43, 47, 59, 67, 71, 79, 83, 89, 103, 107, 131, 137, 139, 167, 179, 191, 211, 223, 227, 233, 239, 251, 263, 271, 281, 283, 311, 313, 331, 347, 359, 367, 379, 383, 409, 419, 431, 439, 443, 457, 463, 467, 479, 499, 503, 521, 547, 563, 569

Offset: 1

Leroy Quet, Sep 14 2009

nonn

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

Cf. A000005, A008328, A036537, A165319, A165320.

isA000079 := proc(n) RETURN( n=1 or numtheory[factorset](n) = {2}) ; end: A165318 := proc(n) if n = 1 then 2; else p := nextprime(procname(n-1)) ; while not isA000079(numtheory[tau](p-1)) do p := nextprime(p) ; od; p ; fi; end: seq(A165318(n),n=1..90) ; # R. J. Mathar, Sep 18 2009

Select[Prime[Range[200]],IntegerQ[Log[2,DivisorSigma[0,#-1]]]&] (* Harvey P. Dale, Oct 14 2018 *)

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

More terms from R. J. Mathar, Sep 18 2009

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.

Original entry on oeis.org

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

Leroy Quet, Sep 14 2009

nonn

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

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

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

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 *)

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

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

cp's OEIS Frontend

A165318 Primes p where the number of divisors of p-1 is a power of 2.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Extensions