A345741 a(n) = n + (n - 1) * d(n).

1, 4, 7, 13, 13, 26, 19, 36, 33, 46, 31, 78, 37, 66, 71, 91, 49, 120, 55, 134, 101, 106, 67, 208, 97, 126, 131, 190, 85, 262, 91, 218, 161, 166, 171, 351, 109, 186, 191, 352, 121, 370, 127, 302, 309, 226, 139, 518, 193, 344, 251, 358, 157, 478, 271, 496, 281, 286, 175, 768, 181

Offset

1,2

Comments

For all k <= n, add n if k | n, otherwise add 1. For example, a(7) = 7 + 1 + 1 + 1 + 1 + 1 + 7 = 19.

Links

Table of n, a(n) for n=1..61.

Formula

a(n) = Sum_{k=1..n} n^c(n/k), where c(n) = 1 - ceiling(n) + floor(n).

a(p) = 3p - 2 for prime p.

Mathematica

Table[n + (n - 1)*DivisorSigma[0, n], {n, 80}]

Prog

(PARI) a(n) = n + (n-1)*numdiv(n); \\ Michel Marcus, Jun 26 2021

Crossrefs

Cf. A000005.

Sequence in context: A372581 A051456 A283626 * A184864 A031142 A266568

Adjacent sequences: A345738 A345739 A345740 * A345742 A345743 A345744

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 25 2021

Status

approved