A342017 - OEIS

A342017

a(n) = A342007(A327860(n)), where A342007 is multiplicative with a(p^e) = p^floor(e/p), and A327860 is arithmetic derivative of A276086.

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1

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OFFSET

1,8

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to primorial base

FORMULA

a(n) = A342007(A327860(n)) = A342007(A003415(A276086(n))).

MATHEMATICA

Block[{b = MixedRadix[Reverse@ Prime@ Range@ 12]}, Array[Function[k, Times @@ Map[#1^Floor[#2/#1] & @@ # &, FactorInteger[#]] &@ If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]] ] &@ Abs[Times @@ Power @@@ # &@ Transpose@{Prime@ Range@ Length@ k, Reverse@ k}]]@ IntegerDigits[#, b] &, 105]] (* Michael De Vlieger, Mar 12 2021 *)

PROG

(PARI)

A327860(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= (p^e); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };

A342007(n) = { my(f = factor(n)); for(k=1, #f~, f[k, 2] = floor(f[k, 2]/f[k, 1])); factorback(f); };

A342017(n) = A342007(A327860(n));

CROSSREFS

Cf. A003415, A276086, A327860, A342007, A342018 (positions of terms > 1).

Cf. also A341997.

Sequence in context: A191004 A191358 A204133 * A062378 A073753 A290602

Adjacent sequences: A342014 A342015 A342016 * A342018 A342019 A342020

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 04 2021

STATUS

approved