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A343657
Sum of number of divisors of x^y for each x >= 1, y >= 0, x + y = n.
6
1, 2, 4, 7, 12, 18, 27, 39, 56, 77, 103, 134, 174, 223, 283, 356, 445, 547, 666, 802, 959, 1139, 1344, 1574, 1835, 2128, 2454, 2815, 3213, 3648, 4126, 4653, 5239, 5888, 6608, 7407, 8298, 9288, 10385, 11597, 12936, 14408, 16025, 17799, 19746, 21882, 24221
OFFSET
1,2
FORMULA
a(n) = Sum_{k=1..n} A000005(k^(n-k)).
EXAMPLE
The a(7) = 27 divisors:
1 32 81 64 25 6 1
16 27 32 5 3
8 9 16 1 2
4 3 8 1
2 1 4
1 2
1
MATHEMATICA
Total/@Table[DivisorSigma[0, k^(n-k)], {n, 30}, {k, n}]
PROG
(Python 3.8+)
from math import prod
from sympy import factorint
def A343657(n): return 1 if n == 1 else 2 + sum((prod(d*(n-k)+1 for d in factorint(k).values())) for k in range(2, n)) # Chai Wah Wu, Jun 03 2021
CROSSREFS
Antidiagonal row sums (row sums of the triangle) of A343656.
Dominated by A343661.
A000005(n) counts divisors of n.
A000312(n) = n^n.
A007318(n,k) counts k-sets of elements of {1..n}.
A009998(n,k) = n^k (as an array, offset 1).
A059481(n,k) counts k-multisets of elements of {1..n}.
A343658(n,k) counts k-multisets of divisors of n.
Sequence in context: A049703 A175812 A002621 * A363211 A033500 A003318
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 29 2021
STATUS
approved