A324886 a(n) = A276086(A108951(n)).

2, 3, 5, 9, 7, 25, 11, 15, 35, 49, 13, 625, 17, 121, 117649, 225, 19, 1225, 23, 2401, 1771561, 169, 29, 875, 717409, 289, 55, 14641, 31, 184877, 37, 21, 4826809, 361, 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

Offset: 1

Author

Antti Karttunen, Mar 30 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..2310
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to primorial base
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A034386, A108951, A117366, A276086, A324887, A324888, A324896, A329047, A342920, A344592, A346106, A346107.

Permutation of A324576.

Cf. also A346105.

Programs

Mathematica

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 *)
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];
(* b is A108951 *)
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;
a[n_] := A276086[b[n]];
Array[a, 100] (* Jean-François Alcover, Dec 01 2021, after _Antti Karttunen in A296086 *)

PARI

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
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; };
A324886(n) = A276086(A108951(n));

Formula

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

a(n) = A117366(n) * A324896(n).

A001222(a(n)) = A324888(n).

A020639(a(n)) = A117366(n).

A032742(a(n)) = A324896(n).

a(A000040(n)) = A000040(1+n).

From Antti Karttunen, Jul 09 2021: (Start)

For n > 1, a(n) = A003961(A329044(n)).

a(n) = A346091(n) * A344592(n).

a(n) = A346106(n) / A346107(n).

A003415(a(n)) = A329047(n).

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

A342001(a(n)) = A342920(n) = A329047(n) / A344592(n).

(End)