A134675 Row sums of triangle A134674.

1, 4, 9, 15, 25, 30, 49, 55, 76, 80, 121, 112, 169, 154, 201, 207, 289, 237, 361, 310, 395, 374, 529, 420, 606, 520, 661, 604, 841, 618, 961, 799, 975, 884, 1165, 919, 1369, 1102, 1361, 1202, 1681, 1206, 1849, 1480, 1761, 1610, 2209, 1612, 2360, 1843, 2325, 2062, 2809, 2010, 2897, 2368, 2903, 2552, 3481

Offset: 1

Author

Gary W. Adamson, Nov 05 2007

Keywords

• nonn

Examples

			a(4) = 15 = sum of row 4 terms of triangle A134674: (4, + 3 + 4 + 4).
		

Links

• John Mason, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001065, A007434, A134674.

Programs

Mathematica

f1[p_, e_] := p^(2*e) - p^(2*e-2); f2[p_, e_] := (p^(e+1)-1)/(p-1); a[1] = 1; a[n_] := Times @@ f1 @@@ (f = FactorInteger[n]) + Times @@ f2 @@@ f - n; Array[a, 60] (* Amiram Eldar, Aug 22 2023 *)

PARI

a(n) = sumdiv(n,d,d^2*moebius(n/d)+d)-n /* Max Alekseyev, Jan 07 2015 */

Formula

For n>1, a(n) = n^2 iff n is prime.

a(n) = A007434(n) + A001065(n). - Conjectured by John Mason and proved by Max Alekseyev, Jan 07 2015

Extensions

More terms from John Mason, Jan 07 2015