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

Author

Jaroslav Krizek, Apr 02 2010

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A007955, A062758.

Programs

Mathematica

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

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

Formula

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

Extensions

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