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A174939
a(n) = Sum_{k<=n} A007955(k) * A007955(k) = Sum_{k<=n} A007955(k)^2, where A007955(m) = product of divisors of m.
2
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
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
Sequence in context: A306751 A305341 A316611 * A320800 A321315 A203225
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Apr 02 2010
EXTENSIONS
a(27) and beyond from Michael S. Branicky, May 03 2022
STATUS
approved