A324886 - OEIS

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

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OFFSET

1,1

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

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)

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 *)

PROG

(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));

CROSSREFS

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

Permutation of A324576.

Cf. also A346105.

Sequence in context: A045965 A323390 A346096 * A277332 A342456 A100674

Adjacent sequences: A324883 A324884 A324885 * A324887 A324888 A324889

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 30 2019

STATUS

approved