A174934 a(n) = Sum_{k<=n} A007955(k) * A000027(n-k+1) = Sum_{k<=n} A007955(k) * (n-k+1), where A007955(m) = product of divisors of m.

1, 4, 10, 24, 43, 98, 160, 286, 439, 692, 956, 2948, 4953, 7154, 9580, 13030, 16497, 25796, 35114, 52432, 70191, 88434, 106700, 456742, 806909, 1157752, 1509324, 1882848, 2256401, 3439954, 4623538, 5839890, 7057331, 8275928, 9495750, 20793268, 32090823, 43389822

Offset

1,2

Links

Table of n, a(n) for n=1..38.

Example

For n = 4, A007955(n) = b(n): a(4) = b(1)*4 + b(2)*3 + b(3)* 2 + b(4)*1 = 1*4 + 2*3 + 3*2 + 8*1 = 24.

Mathematica

a[n_] := Sum[k^(DivisorSigma[0, k]/2) * (n-k+1), {k, 1, n}]; Array[a, 50] (* Amiram Eldar, Aug 06 2024 *)

Crossrefs

Cf. A000027, A007955.

Sequence in context: A274019 A008258 A008251 * A083168 A143696 A058514

Adjacent sequences: A174931 A174932 A174933 * A174935 A174936 A174937

Keyword

nonn

Author

Jaroslav Krizek, Apr 02 2010

Extensions

More terms from Amiram Eldar, Aug 06 2024

Status

approved