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A358216
Inverse Möbius transform of A327936, where A327936 is multiplicative with a(p^e) = p if e >= p, otherwise 1.
2
1, 2, 2, 4, 2, 4, 2, 6, 3, 4, 2, 8, 2, 4, 4, 8, 2, 6, 2, 8, 4, 4, 2, 12, 3, 4, 6, 8, 2, 8, 2, 10, 4, 4, 4, 12, 2, 4, 4, 12, 2, 8, 2, 8, 6, 4, 2, 16, 3, 6, 4, 8, 2, 12, 4, 12, 4, 4, 2, 16, 2, 4, 6, 12, 4, 8, 2, 8, 4, 8, 2, 18, 2, 4, 6, 8, 4, 8, 2, 16, 9, 4, 2, 16, 4, 4, 4, 12, 2, 12, 4, 8, 4, 4, 4, 20, 2, 6, 6, 12
OFFSET
1,2
COMMENTS
Multiplicative because A327936 is.
FORMULA
a(n) = Sum_{d|n} A327936(d).
For all n >= 0, a(A276086(n)) = A324655(n).
For all n >= 1, a(n) >= A000005(n).
Multiplicative with a(p^e) = e + 1 if e < p, and p*(e - p + 2) otherwise. - Amiram Eldar, Nov 30 2022
MATHEMATICA
f[p_, e_] := If[e < p, e + 1, p*(e - p + 2)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Nov 30 2022 *)
PROG
(PARI)
A327936(n) = { my(f = factor(n)); for(k=1, #f~, f[k, 2] = (f[k, 2]>=f[k, 1])); factorback(f); };
A358216(n) = sumdiv(n, d, A327936(d));
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Nov 30 2022
STATUS
approved