A181149 -id:A181149 - cp's OEIS frontend

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

Michel Marcus, Sep 05 2015

nonn

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

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

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

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;}

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

A261888 Positive integers n such that there is no triple of primes (p, q, r) satisfying p+q^2+r^3=n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 18, 21, 26, 27, 32, 37, 45, 51, 61, 66, 82, 108, 127, 178, 186, 192, 234, 252, 276, 306, 332, 336, 351, 402, 468, 582, 606, 612, 622, 642, 666, 702, 712, 738, 762, 798, 816, 822, 864, 882, 906, 930, 996, 1018, 1032

Offset: 1

Michel Marcus, Sep 05 2015

nonn

			For p=2, p+p^2+p^3 = 14 = A181149(1), so 14 is the first value not to be in the sequence.

Cf. A181149, A261887.

nbt(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;}
isok(n) = nbt(n)==0;

cp's OEIS Frontend

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

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