cp's OEIS Frontend

A353571 Prime-shifted variant of A342001: a(n) = A349905(n) / A003557(A003961(n)).

%I A353571 #12 Apr 29 2022 15:55:47
%S A353571 0,1,1,2,1,8,1,3,2,10,1,13,1,14,12,4,1,11,1,17,16,16,1,18,2,20,3,25,1,
%T A353571 71,1,5,18,22,18,16,1,26,22,24,1,103,1,29,19,32,1,23,2,13,24,37,1,14,
%U A353571 20,36,28,34,1,106,1,40,27,6,24,119,1,41,34,131,1,21,1,44,17,49,24,151,1,31,4,46,1,158,26,50,36
%N A353571 Prime-shifted variant of A342001: a(n) = A349905(n) / A003557(A003961(n)).
%H A353571 Antti Karttunen, <a href="/A353571/b353571.txt">Table of n, a(n) for n = 1..20000</a>
%H A353571 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A353571 a(n) = A342001(A003961(n)) = A349905(n) / A003557(A003961(n)).
%F A353571 For all n >= 1, a(n) >= A342001(n).
%o A353571 (PARI)
%o A353571 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A353571 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A353571 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
%o A353571 A353571(n) = { my(s=A003961(n)); (A003415(s)/A003557(s)); };
%Y A353571 Cf. A003415, A003557, A003961, A342001, A349905, A353572.
%K A353571 nonn
%O A353571 1,4
%A A353571 _Antti Karttunen_, Apr 27 2022