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A371085 Nonsquarefree numbers k such that A003415(k) divides A276086(k), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

%I A371085 #7 Mar 13 2024 12:13:44
%S A371085 9,25,49,207,333,375,531,605,819,1331,1719,1850,2057,2205,2299,2331,
%T A371085 2853,4491,4575,5746,6413,6591,6655,9559,9873,12947,13426,14063,15851,
%U A371085 15886,16425,17303,19125,19942,20531,21609,21970,22139,26667,30923,33975,34731,35379,37251,37873,38350,38599,39075,41743,44447,45950
%N A371085 Nonsquarefree numbers k such that A003415(k) divides A276086(k), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.
%H A371085 Antti Karttunen, <a href="/A371085/b371085.txt">Table of n, a(n) for n = 1..7575</a>
%H A371085 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%o A371085 (PARI)
%o A371085 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A371085 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A371085 A358220(n) = if(n<2, 0, !(A276086(n)%A003415(n)));
%o A371085 isA371085(n) = (!issquarefree(n)&&A358220(n));
%Y A371085 Intersection of A013929 and A358221 (or A358222).
%Y A371085 Subsequence of A371083, and of A371086.
%Y A371085 Cf. A003415, A276086.
%K A371085 nonn
%O A371085 1,1
%A A371085 _Antti Karttunen_, Mar 12 2024