A276045 -id:A276045 - cp's OEIS frontend

A276305 Primes p such that d(p*(2p+1)) = 12 where d(n) is the number of divisors of n (A000005).

31, 37, 73, 103, 137, 139, 181, 193, 211, 269, 373, 433, 463, 541, 563, 571, 587, 733, 751, 859, 887, 929, 1021, 1129, 1151, 1381, 1399, 1489, 1637, 1723, 1993, 2053, 2083, 2087, 2237, 2521, 2621, 2731, 2837, 2843, 2909, 3109, 3137, 3209, 3271, 3313, 3323, 3343, 3541, 4091

Offset: 1

Anthony Hernandez, Aug 29 2016

nonn

Conjecture: this sequence is infinite.

Each number p * (2p + 1) is of the form p * q * r^2 but not of the form p * q^5. - David A. Corneth, Aug 30 2016

			Consider 31. Then 31*((2*31)+1) = 2*(31^2) + 31 = 1953 = 3*3*7*31 and d(1953) = 12.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000005, A005384, A030630, A054753, A276045, A276307.

[n: n in [0..5000] | NumberOfDivisors(2*n+1) eq 6 and IsPrime(n)]; // Vincenzo Librandi, Aug 30 2016

Select[Prime@ Range@ 576, DivisorSigma[0, # (2 # + 1)] == 12 &] (* Michael De Vlieger, Aug 30 2016 *)

is(n) = ispseudoprime(n) && numdiv(n*(2*n+1))==12 \\ Felix Fröhlich, Aug 29 2016

is(n)=numdiv(2*n+1)==6 && isprime(n) \\ Charles R Greathouse IV, Aug 29 2016

More terms from Antti Karttunen, Aug 29 2016

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

Original entry on oeis.org

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

Anthony Hernandez, Aug 29 2016

nonn

Conjecture: this sequence is infinite.

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

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

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

Cf. A005384, A030634, A276045, A276305.

[n: n in [0..2000] | NumberOfDivisors(2*n+1) eq 8 and IsPrime(n)]; // Vincenzo Librandi, Aug 30 2016

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

lista(nn) = forprime (p=2, nn, if (numdiv(p*(2*p+1)) == 16, print1(p, ", "))); \\ Michel Marcus, Aug 29 2016

is(n)=numdiv(2*n+1)==8 && isprime(n) \\ Charles R Greathouse IV, Aug 29 2016

Corrected and extended by Michel Marcus, Aug 29 2016

cp's OEIS Frontend

A276305 Primes p such that d(p*(2p+1)) = 12 where d(n) is the number of divisors of n (A000005).

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

PARI

Extensions