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
KEYWORD
nonn
AUTHOR
Anthony Hernandez, Aug 29 2016
EXTENSIONS
More terms from Antti Karttunen, Aug 29 2016
STATUS
approved