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 A319076 Square array T(n,k) read by antidiagonal upwards in which column k lists the partial sums of the powers of the k-th prime, n >= 0, k >= 1. 2
 1, 3, 1, 7, 4, 1, 15, 13, 6, 1, 31, 40, 31, 8, 1, 63, 121, 156, 57, 12, 1, 127, 364, 781, 400, 133, 14, 1, 255, 1093, 3906, 2801, 1464, 183, 18, 1, 511, 3280, 19531, 19608, 16105, 2380, 307, 20, 1, 1023, 9841, 97656, 137257, 177156, 30941, 5220, 381, 24, 1, 2047, 29524, 488281, 960800, 1948717 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS T(n,k) is also the sum of the divisors of the n-th nonnegative power of the k-th prime, n >= 0, k >= 1. LINKS FORMULA T(n,k) = A000203(A000040(k)^n). T(n,k) = Sum_{j=0..n} A000040(k)^j. T(n,k) = Sum_{j=0..n} A319075(j,k). T(n,k) = (A000040(k)^(n+1) - 1)/(A000040(k) - 1). T(n,k) = (A000040(k)^(n+1) - 1)/A006093(k). EXAMPLE The corner of the square array is as follows:          A126646 A003462 A003463  A023000    A016123    A091030     A091045 A000012        1,      1,      1,       1,         1,         1,          1, ... A008864        3,      4,      6,       8,        12,        14,         18, ... A060800        7,     13,     31,      57,       133,       183,        307, ... A131991       15,     40,    156,     400,      1464,      2380,       5220, ... A131992       31,    121,    781,    2801,     16105,     30941,      88741, ... A131993       63,    364,   3906,   19608,    177156,    402234,    1508598, ... .......      127,   1093,  19531,  137257,   1948717,   5229043,   25646167, ... .......      255,   3280,  97656,  960800,  21435888,  67977560,  435984840, ... .......      511,   9841, 488281, 6725601, 235794769, 883708281, 7411742281, ... ... PROG (PARI) T(n, k) = sigma(prime(k)^n); \\ Michel Marcus, Sep 13 2018 CROSSREFS Rows 0-5: A000012, A008864, A060800, A131991, A131992, A131993. Columns 1-15: A126646, A003462, A003463, A023000, A016123, A091030, A091045, A218722, A218726, A218732, A218734, A218740, A218744, A218746, A218750. Main diagonal gives A319074. Cf. A000079, A000244, A000351, A000420, A001020, A001022, A001026, A001029, A009967, A009973, A009975, A009981, A009985, A009987, A009991. Cf. A000040, A000203, A006093, A319075. Sequence in context: A110814 A275599 A210038 * A286513 A193970 A274510 Adjacent sequences:  A319073 A319074 A319075 * A319077 A319078 A319079 KEYWORD nonn,tabl,easy AUTHOR Omar E. Pol, Sep 09 2018 STATUS approved

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Last modified January 21 11:10 EST 2020. Contains 331105 sequences. (Running on oeis4.)