A358223 - OEIS

%I #15 Oct 23 2023 02:02:17

%S 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,

%T 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,

%U 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

%N Inverse Möbius transform of A181819, prime shadow function.

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

%H Michael De Vlieger, <a href="/A358223/b358223.txt">Table of n, a(n) for n = 1..16384</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.

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

%F Multiplicative with a(p^e) = 1 + Sum_{k=1..e} prime(k) = A014284(e+1). - _Amiram Eldar_, Oct 23 2023

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

%o (PARI)

%o A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));

%o A358223(n) = sumdiv(n,d,A181819(d));

%Y Cf. A014284, A046523, A181819.

%K nonn,mult

%O 1,2

%A _Antti Karttunen_, Nov 30 2022