OFFSET
1,2
FORMULA
a(n) = usigma(n) * 2^omega(n).
a(n) = Sum_{d|n, gcd(d, n/d) = 1} usigma(d) * usigma(n/d).
a(n) = Sum_{d|n, gcd(d, n/d) = 1} d * 2^omega(d) * 2^omega(n/d).
a(n) = Sum_{d|n, gcd(d, n/d) = 1} A343525(d).
MATHEMATICA
a[1] = 1; a[n_] := Times @@ (2 (#[[1]]^#[[2]] + 1) & /@ FactorInteger[n]); Table[a[n], {n, 64}]
PROG
(PARI) a(n) = my(f=factor(n)); for (k=1, #f~, f[k, 1] = 2*f[k, 1]^f[k, 2] + 2; f[k, 2] = 1); factorback(f); \\ Michel Marcus, Apr 20 2021
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Ilya Gutkovskiy, Apr 20 2021
STATUS
approved