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A344592 a(n) = A003557(A276086(A108951(n))).

%I A344592 #15 Jul 20 2021 03:26:04
%S A344592 1,1,1,3,1,5,1,1,1,7,1,125,1,11,16807,15,1,35,1,343,161051,13,1,25,
%T A344592 9317,17,1,1331,1,2401,1,1,371293,19,253333223,42875,1,23,1419857,1,1,
%U A344592 1,1,2197,14641,29,1,49,371293,6684099653,2476099,4913,1,55,37349,19487171,6436343,31,1,5929,1,37,20449,21,582622237229761,1792160394037
%N A344592 a(n) = A003557(A276086(A108951(n))).
%H A344592 Antti Karttunen, <a href="/A344592/b344592.txt">Table of n, a(n) for n = 1..2310</a>
%H A344592 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%H A344592 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A344592 a(n) = A328572(A108951(n)) = A003557(A324886(n)) = A003557(A276086(A108951(n))).
%F A344592 a(n) = A329047(n) / A342920(n).
%F A344592 a(n) = A085731(A324886(n)) = gcd(A324886(n), A329047(n)) = A324886(n) / A346091(n). - _Antti Karttunen_, Jul 09 2021
%t A344592 Block[{b = MixedRadix[Reverse@ Prime@ Range@ 20]}, Array[#/(Times @@ FactorInteger[#][[All, 1]]) &@ Apply[Times, Power @@@ #] &@ Transpose@ {Prime@ Range@ Length@ #, Reverse@ #} &@ IntegerDigits[#, b] &@ Apply[Times, Map[(Times @@ Prime@ Range@ PrimePi@ #1)^#2 & @@ # &, FactorInteger[#]]] &, 66]] (* _Michael De Vlieger_, Jul 14 2021 *)
%o A344592 (PARI)
%o A344592 A034386(n) = prod(i=1, primepi(n), prime(i));
%o A344592 A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) }; \\ From A108951
%o A344592 A328572(n) = { my(m=1, p=2); while(n, if(n%p, m *= p^((n%p)-1)); n = n\p; p = nextprime(1+p)); (m); };
%o A344592 A344592(n) = A328572(A108951(n));
%o A344592 (PARI)
%o A344592 A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); }; \\ From A003557
%o A344592 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A344592 A344592(n) = A003557(A276086(A108951(n)));
%Y A344592 Cf. A003557, A085731, A108951, A276086, A324886, A328572, A329047, A342002, A342920, A346091, A346092 [= A276085(a(n))].
%Y A344592 Cf. A344591 (positions of ones), A344593 (rgs-transform).
%K A344592 nonn
%O A344592 1,4
%A A344592 _Antti Karttunen_, May 26 2021