A358223 Inverse Möbius transform of A181819, prime shadow function.

1, 3, 3, 6, 3, 9, 3, 11, 6, 9, 3, 18, 3, 9, 9, 18, 3, 18, 3, 18, 9, 9, 3, 33, 6, 9, 11, 18, 3, 27, 3, 29, 9, 9, 9, 36, 3, 9, 9, 33, 3, 27, 3, 18, 18, 9, 3, 54, 6, 18, 9, 18, 3, 33, 9, 33, 9, 9, 3, 54, 3, 9, 18, 42, 9, 27, 3, 18, 9, 27, 3, 66, 3, 9, 18, 18, 9, 27, 3, 54, 18, 9, 3, 54, 9, 9, 9, 33, 3, 54

Offset

1,2

Comments

Multiplicative and dependent only on the prime signature (A046523) because also A181819 is.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..16384

Index entries for sequences computed from exponents in factorization of n.

Formula

a(n) = Sum_{d|n} A181819(d).

Multiplicative with a(p^e) = 1 + Sum_{k=1..e} prime(k) = A014284(e+1). - Amiram Eldar, Oct 23 2023

Mathematica

f[n_] := f[n] = Times @@ Prime@ FactorInteger[n][[All, -1]]; Array[DivisorSum[#, f] - 1 &, 90] (* Michael De Vlieger, Nov 30 2022 *)

Prog

(PARI)
A181819(n) = factorback(apply(e->prime(e), (factor(n)[, 2])));
A358223(n) = sumdiv(n, d, A181819(d));

Crossrefs

Cf. A014284, A046523, A181819.

Sequence in context: A307000 A007425 A260152 * A130695 A308083 A181788

Adjacent sequences: A358220 A358221 A358222 * A358224 A358225 A358226

Keyword

nonn,mult

Author

Antti Karttunen, Nov 30 2022

Status

approved