A261887 Number of triples of primes (p,q,r) that satisfy p+q^2+r^3=n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 2, 2, 3, 0, 3, 1, 2, 2, 1, 2, 2, 0, 2, 1, 2, 2, 2, 0, 1, 2, 3, 3, 1, 1, 1, 4, 3, 0, 3, 1, 3, 3, 0, 1, 2, 1, 3, 2, 1, 2, 3, 1, 3, 1, 3, 3, 2, 2, 0, 4, 2, 1, 2, 1, 2, 3, 2

Offset

1,19

Links

Table of n, a(n) for n=1..90.

Ana Rechtman, Août 2015, 4e défi, Images des Mathématiques, CNRS, 2015.

Formula

G.f.: (Sum_{i>=1} x^prime(i))*(Sum_{j>=1} x^(prime(j)^2))*(Sum_{k>=1} x^(prime(k)^3)). - Ilya Gutkovskiy, Feb 06 2017

Example

For p=2, p+p^2+p^3 = 14 = A181149(1), so a(14)=1.

Prog

(PARI) a(n) = {nb = 0; forprime(p=2, n, forprime(q=2, n, if (p+q^2 > n, break); forprime(r=2, n, if (p+q^2+r^3 > n, break); if (p+q^2+r^3 == n, nb++); ); ); ); nb; }

Crossrefs

Cf. A181149 (p+p^2+p^3 with p prime), A261888.

Sequence in context: A321927 A016194 A258139 * A037871 A037853 A255237

Adjacent sequences: A261884 A261885 A261886 * A261888 A261889 A261890

Keyword

nonn

Author

Michel Marcus, Sep 05 2015

Status

approved