OFFSET
1,2
COMMENTS
In other words, in prime factorization of n, replace prime(i) by prime(k*i).
For any k >= 1, n -> A(n, k) is completely multiplicative.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..11325 (antidiagonals n = 1..150 flattened)
FORMULA
EXAMPLE
Square array A(n, k) begins:
n\k| 1 2 3 4 5 6 7 8 9 10
------------------------------------------------------------
1| 1 1 1 1 1 1 1 1 1 1
2| 2 3 5 7 11 13 17 19 23 29
3| 3 7 13 19 29 37 43 53 61 71
4| 4 9 25 49 121 169 289 361 529 841
5| 5 13 23 37 47 61 73 89 103 113
6| 6 21 65 133 319 481 731 1007 1403 2059
7| 7 19 37 53 71 89 107 131 151 173
8| 8 27 125 343 1331 2197 4913 6859 12167 24389
9| 9 49 169 361 841 1369 1849 2809 3721 5041
10| 10 39 115 259 517 793 1241 1691 2369 3277
MAPLE
A:= (n, k)-> mul(ithprime(k*numtheory[pi](i[1]))^i[2], i=ifactors(n)[2]):
seq(seq(A(d+1-k, k), k=1..d), d=1..12); # Alois P. Heinz, Feb 28 2022
MATHEMATICA
Table[If[# == 1, 1, Times @@ Map[Prime[#3*PrimePi[#1]]^#2 & @@ Flatten[{#1, k}] &, FactorInteger[#]]] &[n - k + 1], {n, 11}, {k, n}] // Flatten (* Michael De Vlieger, Feb 28 2022 *)
PROG
(PARI) A(n, k) = { my (f=factor(n)); prod (i=1, #f~, prime(k * primepi(f[i, 1])) ^ f[i, 2]) }
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Rémy Sigrist, Feb 27 2022
STATUS
approved