A294704
Expansion of Product_{k>=1} (1 - k^k*x^k)^(k^k).
Original entry on oeis.org
1, -1, -16, -713, -64711, -9688521, -2165724176, -675843638952, -280752881225790, -149800127712465769, -99844730464906330029, -81300082264515781043363, -79413710307214816810372248, -91652445696245266803423194130
Offset: 0
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nmax = 20; CoefficientList[Series[Product[(1 - k^k*x^k)^(k^k), {k, 1, nmax}], {x, 0, nmax}], x]
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N=20; x='x+O('x^N); Vec(prod(k=1, N, (1-k^k*x^k)^k^k))
A294756
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} 1/(1-j^(k*j)*x^j)^j(k*j) in powers of x.
Original entry on oeis.org
1, 1, 1, 1, 1, 2, 1, 1, 17, 3, 1, 1, 257, 746, 5, 1, 1, 4097, 531698, 66442, 7, 1, 1, 65537, 387424586, 4295533810, 9843731, 11, 1, 1, 1048577, 282429602018, 281475372654922, 95371863223331, 2187951485, 15, 1, 1, 16777217, 205891133143226, 18446744358295025890, 931322857677725493491, 4738477951108288824, 680615166718, 22
Offset: 0
Square array begins:
1, 1, 1, 1, ...
1, 1, 1, 1, ...
2, 17, 257, 4097, ...
3, 746, 531698, 387424586, ...
5, 66442, 4295533810, 281475372654922, ...
A294773
a(n) = Sum_{d|n} d^(d+n+1).
Original entry on oeis.org
1, 33, 2188, 262273, 48828126, 13060753578, 4747561509944, 2251799880796161, 1350851717674586413, 1000000000152587898818, 895430243255237372246532, 953962166441299506564257602, 1192533292512492016559195008118
Offset: 1
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a[n_] := DivisorSum[n, #^(# + n + 1) &]; Array[a, 13] (* Amiram Eldar, Oct 04 2023 *)
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{a(n) = sumdiv(n, d, d^(d+n+1))}
Showing 1-3 of 3 results.