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

1,1

Comments

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

Links

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

Example

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

Mathematica

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

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A276305 (MATCHING-POS 1 1 (lambda (n) (and (= 1 (A010051 n)) (= 12 (A000005 (* n (+ n n 1))))))))
;; Antti Karttunen, Aug 29 2016
(PARI) is(n) = ispseudoprime(n) && numdiv(n*(2*n+1))==12 \\ Felix Fröhlich, Aug 29 2016
(PARI) is(n)=numdiv(2*n+1)==6 && isprime(n) \\ Charles R Greathouse IV, Aug 29 2016
(Magma) [n: n in [0..5000] | NumberOfDivisors(2*n+1) eq 6 and IsPrime(n)]; // Vincenzo Librandi, Aug 30 2016

Crossrefs

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

Sequence in context: A067826 A107013 A107012 * A170853 A260673 A062213

Adjacent sequences: A276302 A276303 A276304 * A276306 A276307 A276308

Keyword

nonn

Author

Anthony Hernandez, Aug 29 2016

Extensions

More terms from Antti Karttunen, Aug 29 2016

Status

approved