cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

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%I A342017 #14 Mar 12 2021 23:49:37
%S A342017 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,
%T A342017 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,
%U A342017 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
%N 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.
%H A342017 Antti Karttunen, <a href="/A342017/b342017.txt">Table of n, a(n) for n = 1..65537</a>
%H A342017 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A342017 a(n) = A342007(A327860(n)) = A342007(A003415(A276086(n))).
%t A342017 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 *)
%o A342017 (PARI)
%o A342017 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); };
%o A342017 A342007(n) = { my(f = factor(n)); for(k=1, #f~, f[k, 2] = floor(f[k, 2]/f[k, 1])); factorback(f); };
%o A342017 A342017(n) = A342007(A327860(n));
%Y A342017 Cf. A003415, A276086, A327860, A342007, A342018 (positions of terms > 1).
%Y A342017 Cf. also A341997.
%K A342017 nonn
%O A342017 1,8
%A A342017 _Antti Karttunen_, Mar 04 2021