A367864 a(n) = Sum_{d|n} d * binomial(n,d).

1, 4, 6, 20, 10, 102, 14, 352, 270, 1370, 22, 8340, 26, 24234, 16410, 110512, 34, 551754, 38, 1944880, 817992, 7760258, 46, 39190392, 265700, 135208502, 42190254, 570003392, 58, 2631501240, 62, 9701577536, 2128920354, 39671306930, 48694870, 179231802444, 74

Offset: 1

Author

Wesley Ivan Hurt, Dec 03 2023

Keywords

• nonn
• easy

Crossrefs

Cf. A056045, A271654.

Programs

Maple

a:= n-> n*add(binomial(n-1, d-1), d=numtheory[divisors](n)):
seq(a(n), n=1..50);  # Alois P. Heinz, Dec 03 2023

Mathematica

Table[Sum[d*Binomial[n, d], {d, Divisors[n]}], {n, 50}]

PARI

a(n) = sumdiv(n, d, d * binomial(n,d)); \\ Michel Marcus, Dec 03 2023

Formula

a(p) = 2p, for p prime.

a(n) = n * A271654(n). - Alois P. Heinz, Dec 03 2023