A099985 a(n) = rad(2n), where rad = A007947.

2, 2, 6, 2, 10, 6, 14, 2, 6, 10, 22, 6, 26, 14, 30, 2, 34, 6, 38, 10, 42, 22, 46, 6, 10, 26, 6, 14, 58, 30, 62, 2, 66, 34, 70, 6, 74, 38, 78, 10, 82, 42, 86, 22, 30, 46, 94, 6, 14, 10, 102, 26, 106, 6, 110, 14, 114, 58, 118, 30, 122, 62, 42, 2, 130, 66, 134, 34, 138, 70, 142, 6

Offset: 1

Author

N. J. A. Sloane, Nov 19 2004

Keywords

• nonn
• easy

Comments

Bisection of A007947.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A007947, A065463, A099984, A204455.

Programs

Maple

with(numtheory): A007947 := proc(n) local i,t1,t2; t1 :=ifactors(n)[2]; t2 := mul(t1[i][1],i=1..nops(t1)); end: seq(A007947(2*n),n=1..78); # Emeric Deutsch, Dec 15 2004

Mathematica

Table[Product[p, {p, Select[Divisors[2 n], PrimeQ]}], {n, 100}] (* Wesley Ivan Hurt, May 08 2022 *)
a[n_] := Times @@ (First /@ FactorInteger[2*n]); Array[a, 100]  (* Amiram Eldar, Nov 19 2022 *)

PARI

A099985(n) = factorback(factorint(n+n)[, 1]); \\ Antti Karttunen, May 08 2022

Formula

a(n) = 2 * A204455(n).

a(n) = A007947(2n). - Wesley Ivan Hurt, May 07 2022

Sum_{k=1..n} a(k) ~ c * n^2, where c = (4/5) * Product_{p prime} (1 - 1/(p*(p+1))) = (4/5) * A065463 = 0.563553... . - Amiram Eldar, Nov 19 2022

Extensions

More terms from Emeric Deutsch, Dec 15 2004

Name changed by Wesley Ivan Hurt, May 07 2022