cp's OEIS Frontend

A353572 Shifted variant of A342002: a(n) = A353571(A276086(n)), where A353571(x) = A003415(A003961(x)) / A003557(A003961(x)) and A276086 is the primorial base exp-function.

%I A353572 #15 Apr 29 2022 15:55:51
%S A353572 0,1,1,8,2,11,1,10,12,71,19,92,2,13,17,86,24,107,3,16,22,101,29,122,4,
%T A353572 19,27,116,34,137,1,14,16,103,27,136,18,131,167,886,244,1117,29,164,
%U A353572 222,1051,299,1282,40,197,277,1216,354,1447,51,230,332,1381,409,1612,2,17,21,118,32,151,25,152,202,991,279
%N A353572 Shifted variant of A342002: a(n) = A353571(A276086(n)), where A353571(x) = A003415(A003961(x)) / A003557(A003961(x)) and A276086 is the primorial base exp-function.
%H A353572 Antti Karttunen, <a href="/A353572/b353572.txt">Table of n, a(n) for n = 0..11550</a>
%H A353572 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A353572 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A353572 a(n) = A353571(A276086(n)).
%F A353572 a(n) = A342002(A276154(n)).
%F A353572 For all n >= 0, a(n) >= A342002(n).
%o A353572 (PARI)
%o A353572 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A353572 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A353572 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
%o A353572 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A353572 A353571(n) = { my(s=A003961(n)); (A003415(s)/A003557(s)); };
%o A353572 A353572(n) = A353571(A276086(n));
%Y A353572 Cf. A003415, A003557, A003961, A276154, A342002, A349905, A353571, A353573 [= gcd(a(n), A342002(n))], A353574.
%K A353572 nonn,base
%O A353572 0,4
%A A353572 _Antti Karttunen_, Apr 27 2022