A354876 -id:A354876 - cp's OEIS frontend

A354875 Dirichlet inverse of A344005, the smallest positive m such that n divides the oblong number m*(m+1).

1, -1, -2, -2, -4, 2, -6, -2, -4, 4, -10, 7, -12, 6, 11, 0, -16, 4, -18, 16, 18, 10, -22, 4, -8, 12, -2, 23, -28, -11, -30, 4, 29, 16, 34, 12, -36, 18, 36, 5, -40, -18, -42, 39, 27, 22, -46, -6, -12, 8, 47, 48, -52, 2, 70, 25, 54, 28, -58, -78, -60, 30, 21, 8, 71, -29, -66, 64, 65, -34, -70, 24, -72, 36, 16, 71, 99

Offset: 1

Antti Karttunen, Jun 12 2022

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

Cf. A002378, A344005, A354876, A354877 (positions of 0's).

Cf. also A345055.

f[n_] := Module[{m = 1}, While[! Divisible[m*(m + 1), n], m++]; m]; a[1] = 1; a[n_] := a[n] = -DivisorSum[n, a[#]*f[n/#] &, # < n &]; Array[a, 100] (* Amiram Eldar, Jun 12 2022 *)

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)));

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA344005(n/d) * a(d).

a(n) = A354876(n) - A344005(n).

cp's OEIS Frontend

A354875 Dirichlet inverse of A344005, the smallest positive m such that n divides the oblong number m*(m+1).

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