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A329600 Smallest number with the same set of distinct prime exponents as A108951(n).

%I A329600 #15 Nov 18 2019 22:03:44
%S A329600 1,2,2,4,2,12,2,8,4,12,2,24,2,12,12,16,2,72,2,24,12,12,2,48,4,12,8,24,
%T A329600 2,360,2,32,12,12,12,144,2,12,12,48,2,360,2,24,24,12,2,96,4,72,12,24,
%U A329600 2,432,12,48,12,12,2,720,2,12,24,64,12,360,2,24,12,360,2,288,2,12,72,24,12,360,2,96,16,12,2,720,12,12,12,48,2,2160,12,24,12,12,12
%N A329600 Smallest number with the same set of distinct prime exponents as A108951(n).
%H A329600 Antti Karttunen, <a href="/A329600/b329600.txt">Table of n, a(n) for n = 1..20000</a>
%H A329600 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A329600 a(n) = A328400(A108951(n)) = A181821(A007947(A122111(n)))
%F A329600 a(n) = A181821(A329607(n)) = A181821(A122111(A071364(n))).
%t A329600 Array[Times @@ MapIndexed[Prime[#2[[1]]]^#1 &, Reverse[Flatten[Cases[FactorInteger[#], {p_, k_} :> Table[PrimePi[p], {k}]]]]] &[Times @@ FactorInteger[#][[All, 1]]] &@ If[# == 1, 1, Times @@ Prime@ FactorInteger[#][[All, -1]]] &[Times @@ Map[#1^#2 & @@ # &, FactorInteger[#] /. {p_, e_} /; e > 0 :> {Times @@ Prime@ Range@ PrimePi@ p, e}]] &, 105] (* _Michael De Vlieger_, Nov 18 2019, after _Gus Wiseman_ at A181821 *)
%o A329600 (PARI)
%o A329600 A007947(n) = factorback(factorint(n)[, 1]);
%o A329600 A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
%o A329600 A181821(n) = { my(f=factor(n),p=0,m=1); forstep(i=#f~,1,-1,while(f[i,2], f[i,2]--; m *= (p=nextprime(p+1))^primepi(f[i,1]))); (m); };
%o A329600 A328400(n) = A181821(A007947(A181819(n)));
%o A329600 A034386(n) = prod(i=1, primepi(n), prime(i));
%o A329600 A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
%o A329600 A329600(n) = A328400(A108951(n));
%Y A329600 Cf. A007947, A034386, A071364, A108951, A122111, A181819, A181821, A328400, A329607.
%Y A329600 Cf. A077462 (rgs-transform, from its term a(1)=1 onward).
%K A329600 nonn
%O A329600 1,2
%A A329600 _Antti Karttunen_, Nov 17 2019