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 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. 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 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

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Last modified April 10 19:06 EDT 2021. Contains 342853 sequences. (Running on oeis4.)