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

1,2

Links

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

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A001065, A007434, A134674.

Sequence in context: A065893 A052116 A109641 * A050530 A278021 A102084

Adjacent sequences: A134672 A134673 A134674 * A134676 A134677 A134678

Keyword

nonn

Author

Gary W. Adamson, Nov 05 2007

Extensions

More terms from John Mason, Jan 07 2015

Status

approved