A351942 - OEIS

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A351942

Arithmetic derivative of A181819(n), where A181819(n) = Product prime(e(i)) when n = Product prime(i)^e(i).

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

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OFFSET

1,6

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences computed from exponents in factorization of n

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])));

A351942(n) = A003415(A181819(n));

CROSSREFS

Cf. A003415, A181819, A351944, A351945.

Coincides with A351943 on the positions given by A130091.

Sequence in context: A155826 A273711 A340227 * A351230 A173675 A364360

Adjacent sequences: A351939 A351940 A351941 * A351943 A351944 A351945

KEYWORD

nonn

AUTHOR

Antti Karttunen, Apr 02 2022

STATUS

approved