A354876 Sum of A344005 and its Dirichlet inverse, where A344005(n) is the smallest positive m such that n divides the oblong number m*(m+1).

2, 0, 0, 1, 0, 4, 0, 5, 4, 8, 0, 10, 0, 12, 16, 15, 0, 12, 0, 20, 24, 20, 0, 12, 16, 24, 24, 30, 0, -6, 0, 35, 40, 32, 48, 20, 0, 36, 48, 20, 0, -12, 0, 50, 36, 44, 0, 9, 36, 32, 64, 60, 0, 28, 80, 32, 72, 56, 0, -63, 0, 60, 48, 71, 96, -18, 0, 80, 88, -20, 0, 32, 0, 72, 40, 90, 120, -24, 0, 10, 88, 80, 0, -98, 128

Offset: 1

Author

Antti Karttunen, Jun 12 2022

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A344005, A354875.

Cf. also A345065.

Programs

PARI

A344005(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m))); \\ From A344005
memoA354875 = Map();
A354875(n) = if(1==n,1,my(v); if(mapisdefined(memoA354875,n,&v), v, v = -sumdiv(n,d,if(dA344005(n/d)*A354875(d),0)); mapput(memoA354875,n,v); (v)));
A354876(n) = (A344005(n)+A354875(n));

Formula

a(n) = A344005(n) + A354875(n).

a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1A344005(d) * A354875(n/d).