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A360759
a(n) = Sum_{d|n} d^(d+n/d) * binomial(d,n/d).
1
1, 16, 243, 4112, 78125, 1680345, 40353607, 1073766400, 31381060338, 1000000781250, 34522712143931, 1283918489808640, 51185893014090757, 2177953338656796883, 98526125335697265625, 4722366482899710050304, 239072435685151324847153
OFFSET
1,2
LINKS
FORMULA
G.f.: Sum_{k>0} k^k * ( (1 + k*x^k)^k - 1 ).
If p is prime, a(p) = p^(p+2).
MATHEMATICA
a[n_] := DivisorSum[n, #^(# + n/#) * Binomial[#, n/#] &]; Array[a, 20] (* Amiram Eldar, Aug 02 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, d^(d+n/d)*binomial(d, n/d));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, k^k*((1+k*x^k)^k-1)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 19 2023
STATUS
approved