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A329600
Smallest number with the same set of distinct prime exponents as A108951(n).
7
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, 2, 360, 2, 32, 12, 12, 12, 144, 2, 12, 12, 48, 2, 360, 2, 24, 24, 12, 2, 96, 4, 72, 12, 24, 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
OFFSET
1,2
FORMULA
MATHEMATICA
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 *)
PROG
(PARI)
A007947(n) = factorback(factorint(n)[, 1]);
A181819(n) = factorback(apply(e->prime(e), (factor(n)[, 2])));
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); };
A034386(n) = prod(i=1, primepi(n), prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) }; \\ From A108951
CROSSREFS
Cf. A077462 (rgs-transform, from its term a(1)=1 onward).
Sequence in context: A064482 A341699 A294072 * A344226 A305792 A317942
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 17 2019
STATUS
approved