OFFSET
1,2
COMMENTS
Sum of divisors d of n such that n/d == 1 (mod d).
FORMULA
G.f.: Sum_{k>=1} k * x^k / (1 - x^(k^2)).
MAPLE
a:= n-> add(`if`(irem(n/d-1, d)=0, d, 0), d=numtheory[divisors](n)):
seq(a(n), n=1..80); # Alois P. Heinz, Apr 04 2020
MATHEMATICA
nmax = 70; CoefficientList[Series[Sum[k x^k/(1 - x^(k^2)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
Table[DivisorSum[n, # &, Mod[n/# - 1, #] == 0 &], {n, 1, 70}]
PROG
(PARI) A333694(n) = sumdiv(n, d, d*(0==(((n/d)-1)%d))); \\ Antti Karttunen, Apr 04 2020, after the second Mathematica program.
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 04 2020
STATUS
approved