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A336649
Sum of divisors of A336651(n) (odd part of n divided by its largest squarefree divisor).
5
1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 6, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 8, 6, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 6, 1, 1, 1, 1, 1, 40, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 8, 4, 6, 1, 1, 1, 1, 1
OFFSET
1,9
LINKS
FORMULA
Multiplicative with a(2^e) = 1, a(p^1) = 1 and a(p^e) = (p^e - 1)/(p-1) if e > 1.
a(n) = A000203(A336651(n)) = A335341(A000265(n)).
a(n) = A336652(n) / A204455(n).
Dirichlet g.f.: zeta(s-1) * zeta(s) * (1 - 1/(1-2^s+2^(2*s-1))) * Product_{p prime} (1 - 1/p^(s-1) + 1/p^(2*s-1)). - Amiram Eldar, Dec 18 2023
MATHEMATICA
f[2, e_] := 1; f[p_, e_] := (p^e - 1)/(p-1); a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Dec 07 2020 *)
PROG
(PARI) A336649(n) = { my(f=factor(n)); prod(i=1, #f~, if((2==f[i, 1])||(1==f[i, 2]), 1, (((f[i, 1]^(f[i, 2]))-1) / (f[i, 1]-1)))); };
(PARI)
A000265(n) = (n>>valuation(n, 2));
A335341(n) = if(1==n, n, sigma(n/factorback(factorint(n)[, 1])));
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Jul 30 2020
STATUS
approved