A349005 a(n) = Sum_{d|n, d^2>=n} 1+d+n/d.

3, 4, 5, 11, 7, 14, 9, 17, 18, 20, 13, 31, 15, 26, 26, 38, 19, 42, 21, 45, 34, 38, 25, 64, 38, 44, 42, 59, 31, 76, 33, 66, 50, 56, 50, 102, 39, 62, 58, 94, 43, 100, 45, 87, 81, 74, 49, 129, 66, 96, 74, 101, 55, 124, 74, 124, 82, 92, 61, 174, 63, 98, 107, 139, 86, 148

Offset

1,1

Links

Table of n, a(n) for n=1..66.

Roland Bacher, Yet another Proof of an old Hat, arXiv:2111.02788 [math.HO], 2021.

Formula

a(n) = A060866(n) + A038548(n).

Mathematica

a[n_] := DivisorSum[n, 1 + # + n/# &, #^2 >= n &]; Array[a, 100] (* Amiram Eldar, Nov 05 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, if (d^2>=n, d+1+n/d));

Crossrefs

Cf. A038548, A060866.

Sequence in context: A329524 A319067 A224503 * A128920 A006288 A047598

Adjacent sequences: A349002 A349003 A349004 * A349006 A349007 A349008

Keyword

nonn

Author

Michel Marcus, Nov 05 2021

Status

approved