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

1,1

Links

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

Formula

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

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

Prog

(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(d<n, A344005(n/d)*A354875(d), 0)); mapput(memoA354875, n, v); (v)));
A354876(n) = (A344005(n)+A354875(n));

Crossrefs

Cf. A344005, A354875.

Cf. also A345065.

Sequence in context: A349443 A319340 A349389 * A323408 A347099 A347239

Adjacent sequences: A354873 A354874 A354875 * A354877 A354878 A354879

Keyword

sign

Author

Antti Karttunen, Jun 12 2022

Status

approved