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 A319075 Square array T(n,k) read by antidiagonal upwards in which row n lists the n-th powers of primes, hence column k lists the powers of the k-th prime, n >= 0, k >= 1. 6
 1, 2, 1, 4, 3, 1, 8, 9, 5, 1, 16, 27, 25, 7, 1, 32, 81, 125, 49, 11, 1, 64, 243, 625, 343, 121, 13, 1, 128, 729, 3125, 2401, 1331, 169, 17, 1, 256, 2187, 15625, 16807, 14641, 2197, 289, 19, 1, 512, 6561, 78125, 117649, 161051, 28561, 4913, 361, 23, 1, 1024, 19683, 390625, 823543, 1771561, 371293 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS If n = p - 1 where p is prime, then row n lists the numbers with p divisors. The partial sums of column k give the column k of A319076. LINKS FORMULA T(n,k) = A000040(k)^n, n >= 0, k >= 1. EXAMPLE The corner of the square array is as follows:          A000079 A000244 A000351  A000420    A001020    A001022     A001026 A000012        1,      1,      1,       1,         1,         1,          1, ... A000040        2,      3,      5,       7,        11,        13,         17, ... A001248        4,      9,     25,      49,       121,       169,        289, ... A030078        8,     27,    125,     343,      1331,      2197,       4913, ... A030514       16,     81,    625,    2401,     14641,     28561,      83521, ... A050997       32,    243,   3125,   16807,    161051,    371293,    1419857, ... A030516       64,    729,  15625,  117649,   1771561,   4826809,   24137569, ... A092759      128,   2187,  78125,  823543,  19487171,  62748517,  410338673, ... A179645      256,   6561, 390625, 5764801, 214358881, 815730721, 6975757441, ... ... PROG (PARI) T(n, k) = prime(k)^n; CROSSREFS Rows 0-13: A000012, A000040, A001248, A030078, A030514, A050997, A030516, A092759, A179645, A179665, A030629, A079395, A030631, A138031. Other rows n: A030635 (n=16), A030637 (n=18), A137486 (n=22), A137492 (n=28), A139571 (n=30), A139572 (n=36), A139573 (n=40), A139574 (n=42), A139575 (n=46), A173533 (n=52), A183062 (n=58), A183085 (n=60), A261700 (n=100). Columns 1-15: A000079, A000244, A000351, A000420, A001020, A001022, A001026, A001029, A009967, A009973, A009975, A009981, A009985, A009987, A009991. Main diagonal gives A093360. Second diagonal gives A062457. Third diagonal gives A197987. Removing the 1's we have A182944/ A182945. Cf. A006093, A319074, A319076. Sequence in context: A106195 A247023 A051129 * A264871 A067410 A213947 Adjacent sequences:  A319072 A319073 A319074 * A319076 A319077 A319078 KEYWORD nonn,tabl,easy AUTHOR Omar E. Pol, Sep 09 2018 STATUS approved

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Last modified January 19 06:37 EST 2020. Contains 331033 sequences. (Running on oeis4.)