|
|
A354875
|
|
Dirichlet inverse of A344005, the smallest positive m such that n divides the oblong number m*(m+1).
|
|
4
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
LINKS
|
|
|
FORMULA
|
a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A344005(n/d) * a(d).
|
|
MATHEMATICA
|
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 *)
|
|
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)));
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|