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A328242 Numbers k such that A003415(A276086(k)) is a squarefree number, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

%I A328242 #21 Feb 13 2024 14:34:01
%S A328242 1,2,3,4,5,6,7,9,10,11,12,14,15,17,30,32,33,34,35,37,38,39,40,41,42,
%T A328242 43,46,47,60,61,62,63,65,66,67,68,69,71,73,74,75,76,77,210,211,212,
%U A328242 213,215,217,218,219,220,221,223,225,226,227,241,242,243,245,246,247,248,249,250,251,254,255,256,257,270,273,274,275,276,277
%N A328242 Numbers k such that A003415(A276086(k)) is a squarefree number, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.
%C A328242 Numbers n such that A276086(n) is either in A328234 or in A000040 (i.e., it is a prime, in which case n itself is a primorial, A002110).
%H A328242 Antti Karttunen, <a href="/A328242/b328242.txt">Table of n, a(n) for n = 1..10681</a>
%H A328242 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%o A328242 (PARI)
%o A328242 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 A328242 isA328242(n) = issquarefree(A327860(n));
%Y A328242 Positions of 1's in A370130. Subsequence of A370132.
%Y A328242 Cf. A000040, A002110, A003415, A005117, A008966, A276086, A327860, A328234.
%Y A328242 Cf. A328241 (complement).
%Y A328242 Cf. A328233, A328240 (subsequences).
%K A328242 nonn
%O A328242 1,2
%A A328242 _Antti Karttunen_, Oct 10 2019