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A351942
Arithmetic derivative of A181819(n), where A181819(n) = Product prime(e(i)) when n = Product prime(i)^e(i).
6
0, 1, 1, 1, 1, 4, 1, 1, 1, 4, 1, 5, 1, 4, 4, 1, 1, 5, 1, 5, 4, 4, 1, 7, 1, 4, 1, 5, 1, 12, 1, 1, 4, 4, 4, 6, 1, 4, 4, 7, 1, 12, 1, 5, 5, 4, 1, 9, 1, 5, 4, 5, 1, 7, 4, 7, 4, 4, 1, 16, 1, 4, 5, 1, 4, 12, 1, 5, 4, 12, 1, 8, 1, 4, 5, 5, 4, 12, 1, 9, 1, 4, 1, 16, 4, 4, 4, 7, 1, 16, 4, 5, 4, 4, 4, 13, 1, 5, 5, 6, 1, 12
OFFSET
1,6
FORMULA
a(n) = A003415(A181819(n)).
a(n) = A351944(n) * A351945(n).
MATHEMATICA
{0}~Join~Array[If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]] &[Apply[Times, Prime[FactorInteger[#][[All, -1]]]]] &, 101, 2] (* Michael De Vlieger, Apr 03 2022 *)
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A181819(n) = factorback(apply(e->prime(e), (factor(n)[, 2])));
CROSSREFS
Coincides with A351943 on the positions given by A130091.
Sequence in context: A155826 A273711 A340227 * A351230 A173675 A364360
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 02 2022
STATUS
approved