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

1,1

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

Links

Table of n, a(n) for n=1..79.

Formula

a(n^2) = 2.

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

Prog

(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

Crossrefs

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

Sequence in context: A055878 A331654 A346864 * A030304 A248779 A286030

Adjacent sequences: A302687 A302688 A302689 * A302691 A302692 A302693

Keyword

nonn

Author

Juri-Stepan Gerasimov, Apr 11 2018

Extensions

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

Better name from Peter Schorn, Jul 20 2023

Status

approved