OFFSET
1,2
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000
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.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 29 2021
STATUS
approved