A276307 Primes p such that d(p*(2p+1)) = 16 where d(n) is the number of divisors of n (A000005).

67, 97, 127, 199, 227, 229, 241, 277, 307, 313, 331, 379, 397, 457, 467, 499, 547, 617, 619, 647, 709, 727, 739, 757, 773, 797, 823, 829, 857, 883, 977, 1033, 1069, 1093, 1117, 1123, 1171, 1187, 1193, 1201, 1277, 1297, 1303, 1319, 1423, 1447, 1459, 1471, 1483, 1609

Offset

1,1

Comments

Conjecture: this sequence is infinite.

Or, primes p such that d(2p+1)=8. - Zak Seidov, Sep 07 2016

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

Consider 67. Then 67*(2*67+1) = 9045 and d(9045) = 16.

Mathematica

Select[Prime@ Range@ 256, DivisorSigma[0, # (2 # + 1)] == 16 &] (* Michael De Vlieger, Aug 30 2016 *)

Prog

(PARI) lista(nn) = forprime (p=2, nn, if (numdiv(p*(2*p+1)) == 16, print1(p, ", "))); \\ Michel Marcus, Aug 29 2016
(PARI) is(n)=numdiv(2*n+1)==8 && isprime(n) \\ Charles R Greathouse IV, Aug 29 2016
(Magma) [n: n in [0..2000] | NumberOfDivisors(2*n+1) eq 8 and IsPrime(n)]; // Vincenzo Librandi, Aug 30 2016

Crossrefs

Cf. A005384, A030634, A276045, A276305.

Sequence in context: A158848 A232634 A302345 * A260806 A180557 A127732

Adjacent sequences: A276304 A276305 A276306 * A276308 A276309 A276310

Keyword

nonn

Author

Anthony Hernandez, Aug 29 2016

Extensions

Corrected and extended by Michel Marcus, Aug 29 2016

Status

approved