A174939 a(n) = Sum_{k<=n} A007955(k) * A007955(k) = Sum_{k<=n} A007955(k)^2, where A007955(m) = product of divisors of m.

1, 5, 14, 78, 103, 1399, 1448, 5544, 6273, 16273, 16394, 3002378, 3002547, 3040963, 3091588, 4140164, 4140453, 38152677, 38153038, 102153038, 102347519, 102581775, 102582304, 110177896480, 110177912105, 110178369081, 110178900522, 110660790826, 110660791667

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Formula

a(n) = Sum_{k=1..n} A062758(k). - Michel Marcus, May 03 2022

Example

For n = 4, A007955(n) = b(n): a(4) = b(1)^2 + b(2)^2 + b(3)^2 + b(4)^2 = 1^2 + 2^2 + 3^2 + 8^2 = 78.

Mathematica

Accumulate@ Array[#^DivisorSigma[0, #] &, 29] (* Michael De Vlieger, May 03 2022 *)

Prog

(PARI) a(n) = sum(k=1, n, k^numdiv(k)); \\ Michel Marcus, May 03 2022
(Python)
from sympy import divisor_count
from itertools import count, islice
def agen():
    an = 1
    for k in count(2):
        yield an
        an += k**divisor_count(k)
print(list(islice(agen(), 29))) # Michael S. Branicky, May 03 2022

Crossrefs

Cf. A007955, A062758.

Sequence in context: A306751 A305341 A316611 * A320800 A321315 A203225

Adjacent sequences: A174936 A174937 A174938 * A174940 A174941 A174942

Keyword

nonn

Author

Jaroslav Krizek, Apr 02 2010

Extensions

a(27) and beyond from Michael S. Branicky, May 03 2022

Status

approved