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A344760 "Inverted variant" of A342002: a(n) = A342002(A289234(n)).

%I A344760 #11 Jul 13 2021 19:50:57
%S A344760 0,1,1,5,2,7,1,7,8,31,13,41,3,11,14,43,19,53,2,9,11,37,16,47,4,13,17,
%T A344760 49,22,59,1,9,10,41,17,55,12,59,71,247,106,317,26,87,113,331,148,401,
%U A344760 19,73,92,289,127,359,33,101,134,373,169,443,4,15,19,59,26,73,27,89,116,337,151,407,41,117,158,421,193,491,34
%N A344760 "Inverted variant" of A342002: a(n) = A342002(A289234(n)).
%H A344760 Antti Karttunen, <a href="/A344760/b344760.txt">Table of n, a(n) for n = 0..13860</a>
%H A344760 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A344760 a(n) = A342001(A346101(n)) = A342002(A289234(n)).
%o A344760 (PARI)
%o A344760 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A344760 A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A344760 A342001(n) = (A003415(n) / A003557(n));
%o A344760 A346101(n) = { my(pr=1, p=2, m=1); while(n>0, my(d=n%p); if(d>0, m *= p^lift(1/Mod(d, p))); pr *= p; n \= p; p = nextprime(1+p)); return(m); };
%o A344760 A344760(n) = A342001(A346101(n));
%o A344760 (PARI)
%o A344760 A289234(n) = { my(pr=1, p=2, v=0); while(n>0, my (d=n%p); if(d>0, v += pr * lift(1/Mod(d, p))); pr *= p; n \= p; p = nextprime(1+p)); return(v); }; \\ From A289234.
%o A344760 A342002(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= p^(e>0); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };
%o A344760 A344760(n) = A342002(A289234(n));
%Y A344760 Cf. A003415, A003557, A276086, A342001, A342002, A289234, A346101.
%Y A344760 Cf. also A344761, A344762.
%K A344760 nonn,look
%O A344760 0,4
%A A344760 _Antti Karttunen_, Jul 10 2021