A365275 Number of integers k <= n that can be written as k = m^2+p^2 where p is a prime and m is a positive integer.

0, 0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6, 7, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 19, 19, 19, 19, 19, 20, 21, 21, 21, 21, 21, 21, 21

Offset

1,8

Links

Table of n, a(n) for n=1..80.

Andrew Granville, Cihan Sabuncu, and Alisa Sedunova, The multiplication table constant and sums of two squares, arXiv:2308.14911 [math.NT], 2023.

Mathematica

a={}; For[n=1, n<=80, n++, nk=0;  For[k=1, k<=n, k++, flag=1; For[m=1, m<=Sqrt[k]&&flag==1, m++, sp=Sqrt[k-m^2]; If[IntegerQ[sp^2]&&PrimeQ[sp], nk++; flag=0]]]; AppendTo[a, nk]]; a (* Stefano Spezia, Aug 30 2023 *)

Prog

(PARI) isok(k) = my(q); for(i=1, sqrtint(k), if (issquare(q=k-i^2) && isprime(sqrtint(q)), return(1))); return(0);
a(n) = sum(k=1, n, isok(k));

Crossrefs

Cf. A361300.

Sequence in context: A182009 A034463 A259899 * A071996 A072747 A194295

Adjacent sequences: A365272 A365273 A365274 * A365276 A365277 A365278

Keyword

nonn

Author

Michel Marcus, Aug 30 2023

Status

approved