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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. 8
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:
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
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).
Main diagonal gives A093360.
Second diagonal gives A062457.
Third diagonal gives A197987.
Removing the 1's we have A182944/ A182945.
Sequence in context: A356250 A348702 A051129 * A264871 A067410 A213947
KEYWORD
nonn,tabl,easy
AUTHOR
Omar E. Pol, Sep 09 2018
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)