OFFSET
1,3
COMMENTS
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
a(p) = p + 1 for odd primes p (A065091).
EXAMPLE
a(6) = 10 because there are 3 arithmetic divisors of 6 (1, 3 and 6): sigma(1)/tau(1) = 1/1 = 1; sigma(3)/tau(3) = 4/2 = 2; sigma(6)/tau(6) = 12/4 = 3. Sum of this divisors is 10.
MAPLE
f:= proc(n) uses numtheory;
convert(select(t -> sigma(t) mod tau(t) = 0, divisors(n)), `+`) end proc:
map(f, [$1..100]); # Robert Israel, Oct 27 2020
MATHEMATICA
a[n_] := DivisorSum[n, # &, Divisible[DivisorSigma[1, #], DivisorSigma[0, #]] &]; Array[a, 100] (* Amiram Eldar, Oct 15 2020 *)
PROG
(Magma) [&+[d: d in Divisors(n) | IsIntegral(&+Divisors(d) / #Divisors(d))]: n in [1..100]];
(PARI) a(n) = sumdiv(n, d, d*!(sigma(d) % numdiv(d))); \\ Michel Marcus, Oct 15 2020
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Jaroslav Krizek, Oct 14 2020
STATUS
approved