A099984 Bisection of A007947.

1, 3, 5, 7, 3, 11, 13, 15, 17, 19, 21, 23, 5, 3, 29, 31, 33, 35, 37, 39, 41, 43, 15, 47, 7, 51, 53, 55, 57, 59, 61, 21, 65, 67, 69, 71, 73, 15, 77, 79, 3, 83, 85, 87, 89, 91, 93, 95, 97, 33, 101, 103, 105, 107, 109, 111, 113, 115, 39, 119, 11, 123, 5, 127, 129, 131, 133, 15, 137

Offset: 1

Author

N. J. A. Sloane, Nov 19 2004

Keywords

• nonn
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007947, A065463, A099985.

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-1),n=1..78); # Emeric Deutsch, Dec 15 2004

Mathematica

a[n_] := Times @@ (First /@ FactorInteger[2*n-1]); Array[a, 100]  (* Amiram Eldar, Nov 19 2022*)

PARI

a(n) = factorback(factorint(2*n-1)[, 1]); \\ Amiram Eldar, Nov 19 2022

Formula

From Amiram Eldar, Nov 19 2022: (Start)

a(n) = A007947(2*n-1).

Sum_{k=1..n} a(k) ~ c * n^2, where c = (6/5) * Product_{p prime} (1 - 1/(p*(p+1))) = (6/5) * A065463 = 0.8453306... . (End)

Extensions

More terms from Emeric Deutsch, Dec 15 2004

Offset corrected by Amiram Eldar, Nov 19 2022