A302690 a(n) is the smallest integer m such that m*n is a sum of two squares but not one.

2, 1, 6, 2, 1, 3, 14, 1, 2, 1, 22, 6, 1, 7, 3, 2, 1, 1, 38, 1, 42, 11, 46, 3, 2, 1, 6, 14, 1, 3, 62, 1, 66, 1, 7, 2, 1, 19, 3, 1, 1, 21, 86, 22, 1, 23, 94, 6, 2, 1, 3, 1, 1, 3, 11, 7, 114, 1, 118, 3, 1, 31, 14, 2, 1, 33, 134, 1, 138, 7, 142, 1, 1, 1, 6, 38, 154, 3, 158

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 11 2018

Keywords

• nonn

Comments

Previous name was: a(n) is the smallest integer m such that A002828(m*n) = 2.

All terms are squarefree.

Using the sum of two squares theorem it is easy to see that a(n) is either A363340(n) (if A363340(n)*n is not a square) or 2*A363340(n) (if A363340(n)*n is a square). - Peter Schorn, Jul 20 2023

Crossrefs

Cf. A002828, A005117, A007913, A064680, A099304, A302694, A363340.

Programs

Maple

A302690 := proc(n)
    local k ;
    for k from 1 do
        if A002828(k*n) = 2 then
            return k;
        end if;
    end do:
end proc:
seq(A302690(n),n=1..100) ; # R. J. Mathar, Apr 16 2018

PARI

a363340(n) = my(r=1); foreach(mattranspose(factor(n)), f, if(f[1]%4==3&&f[2]%2==1, r*=f[1])); r;
a(n) = my(p=a363340(n)); if(issquare(p*n), 2*p, p); \\ Peter Schorn, Jul 20 2023

Formula

a(n^2) = 2.

Extensions

Name corrected and more terms added by Michel Marcus, Apr 12 2018

Better name from Peter Schorn, Jul 20 2023