cp's OEIS Frontend

A358669 Pointwise product of the arithmetic derivative and the primorial base exp-function.

%I A358669 #24 Jan 11 2023 15:58:51
%S A358669 0,0,3,6,36,18,25,10,180,180,315,90,400,50,675,1200,7200,450,2625,250,
%T A358669 9000,7500,14625,2250,27500,12500,28125,101250,180000,11250,217,14,
%U A358669 1680,588,1197,1512,2100,70,2205,3360,21420,630,7175,350,25200,40950,39375,3150,98000,24500,118125,105000,441000
%N A358669 Pointwise product of the arithmetic derivative and the primorial base exp-function.
%H A358669 Antti Karttunen, <a href="/A358669/b358669.txt">Table of n, a(n) for n = 0..11550</a>
%H A358669 Antti Karttunen, <a href="/A358669/a358669.txt">Data supplement: n, a(n) computed for n = 0..60060</a>
%H A358669 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A358669 a(n) = A003415(n) * A276086(n).
%F A358669 From _Antti Karttunen_, Jan 09 2023: (Start)
%F A358669 a(n) = A327858(n) * A359423(n).
%F A358669 For all n >= 0, A059841(a(n)) = A152822(n).
%F A358669 For all n >= 1, 1-A152822(a(n)) = A353558(n).
%F A358669 For all n >= 0, A121262(a(n)) = A358680(n).
%F A358669 (End)
%o A358669 (PARI)
%o A358669 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A358669 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A358669 A358669(n) = (A003415(n)*A276086(n));
%Y A358669 Cf. A003415, A059841, A121262, A152822, A276086, A327858, A353558, A358680, A358765 (= a(n) mod 60), A359423, A359603 [Dirichlet inverse of 1+a(n)].
%Y A358669 Cf. A016825 (positions of odd terms), A042965 (of even terms), A235992 (of multiples of 4), A067019 (of terms of the form 4k+2), A358748 (of the form 4k+1), A358749 (of the form 4k+3).
%K A358669 nonn
%O A358669 0,3
%A A358669 _Antti Karttunen_, Dec 05 2022