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COMMENTS
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A123944(n) = {19, 28, 87, 99, 104, 196, 203, 210, 222, 228, 231, 238, 281, 328, 367, 499, 579, 620, 888, 967, 1036, 1147, 1204, 1352, 1372, 1403, 1419, 1430, 1470, ...} Numbers n such that A120301(n) differs from A058313(n).
A120301(n) = {1, 1, 5, 7, 47, 37, 319, 533, 1879, 1627, 20417, 18107, 263111, 237371, 52279, 95549, 1768477, 1632341, 167324635, 155685007, ...} Absolute value of numerator of the sum of all matrix elements of n X n matrix M[i,j] = (-1)^(i+j) * i/j, (i,j=1..n).
A058313(n) = {1, 1, 5, 7, 47, 37, 319, 533, 1879, 1627, 20417, 18107, 263111, 237371, 52279, 95549, 1768477, 1632341, 33464927, 155685007, ...} Numerator of the n-th alternating harmonic number, sum ((-1)^(k+1)/k, k=1..n).
The ratio A120301(n)/A058313(n) = 1 for most n.
a(n) is prime for most n.
The first composite ratio a(12) = 119 = 7*17 corresponds to A123944(12) = 238.
Next two composite a(n) = 49 = 7^2 correspond to A123944 = 1470 and A123944 = 10290.
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