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%I #25 Dec 01 2021 11:36:58
%S 2,3,5,9,7,25,11,15,35,49,13,625,17,121,117649,225,19,1225,23,2401,
%T 1771561,169,29,875,717409,289,55,14641,31,184877,37,21,4826809,361,
%U 36226650889,1500625,41,529,24137569,77,43,143,47,28561,1127357,841,53,1715,902613283,514675673281,47045881,83521,59,3025,8254129,214358881,148035889,961,61
%N a(n) = A276086(A108951(n)).
%H Antti Karttunen, <a href="/A324886/b324886.txt">Table of n, a(n) for n = 1..2310</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F a(n) = A276086(A108951(n)).
%F a(n) = A117366(n) * A324896(n).
%F A001222(a(n)) = A324888(n).
%F A020639(a(n)) = A117366(n).
%F A032742(a(n)) = A324896(n).
%F a(A000040(n)) = A000040(1+n).
%F From _Antti Karttunen_, Jul 09 2021: (Start)
%F For n > 1, a(n) = A003961(A329044(n)).
%F a(n) = A346091(n) * A344592(n).
%F a(n) = A346106(n) / A346107(n).
%F A003415(a(n)) = A329047(n).
%F A003557(a(n)) = A344592(n).
%F A342001(a(n)) = A342920(n) = A329047(n) / A344592(n).
%F (End)
%t With[{b = MixedRadix[Reverse@ Prime@ Range@ 120]}, Array[Function[k, Times @@ Power @@@ # &@ Transpose@ {Prime@ Range@ Length@ k, Reverse@ k}]@ IntegerDigits[Apply[Times, Map[#1^#2 & @@ # &, FactorInteger[#] /. {p_, e_} /; e > 0 :> {Times @@ Prime@ Range@ PrimePi@ p, e}]], b] &, 58]] (* _Michael De Vlieger_, Nov 18 2019 *)
%t A276086[n0_] := Module[{m = 1, i = 1, n = n0, p}, While[n > 0, p = Prime[i]; m *= p^Mod[n, p]; n = Quotient[n, p]; i++]; m];
%t (* b is A108951 *)
%t b[n_] := b[n] = Module[{pe = FactorInteger[n], p, e}, If[Length[pe] > 1, Times @@ b /@ Power @@@ pe, {{p, e}} = pe; Times @@ (Prime[Range[ PrimePi[p]]]^e)]]; b[1] = 1;
%t a[n_] := A276086[b[n]];
%t Array[a, 100] (* _Jean-François Alcover_, Dec 01 2021, after _Antti Karttunen in A296086 *)
%o (PARI)
%o A034386(n) = prod(i=1, primepi(n), prime(i));
%o A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) }; \\ From A108951
%o A276086(n) = { my(i=0,m=1,pr=1,nextpr); while((n>0),i=i+1; nextpr = prime(i)*pr; if((n%nextpr),m*=(prime(i)^((n%nextpr)/pr));n-=(n%nextpr));pr=nextpr); m; };
%o A324886(n) = A276086(A108951(n));
%Y Cf. A034386, A108951, A117366, A276086, A324887, A324888, A324896, A329047, A342920, A344592, A346106, A346107.
%Y Permutation of A324576.
%Y Cf. also A346105.
%K nonn
%O 1,1
%A _Antti Karttunen_, Mar 30 2019
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