

A141404


Irregular array: For any prime p that divides n, if the highest power of the prime p that divides n is p^b(n,p), then p^b(n,p) = Sum_{k=1..m} a(n,k), where m is the order of the primepower p^b(n,p) among the primepowers (each being the highest power of each prime q that divides n, where q divides n) when they are ordered by size. Row 1 = (1).


0



1, 2, 3, 4, 5, 2, 1, 7, 8, 9, 2, 3, 11, 3, 1, 13, 2, 5, 3, 2, 16, 17, 2, 7, 19, 4, 1, 3, 4, 2, 9, 23, 3, 5, 25, 2, 11, 27, 4, 3, 29, 2, 1, 2, 31, 32, 3, 8, 2, 15, 5, 2, 4, 5, 37, 2, 17, 3, 10, 5, 3, 41, 2, 1, 4, 43, 4, 7, 5, 4, 2, 21, 47, 3, 13, 49, 2, 23, 3, 14, 4, 9, 53, 2, 25, 5, 6, 7, 1, 3, 16, 2
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OFFSET

1,2


COMMENTS



LINKS



EXAMPLE

The prime factorization of 300 is 2^2 *3^1 *5^2. So the prime powers ordered by size are 3, 4, 25. Therefore row 300 is (3,1,21), because 3=3, 3+1 = 4, 3+1+21 = 25.


PROG

(PARI) { A141404row(n) = my(f); if(n==1, return([1])); f=factorint(n); f=vecsort(vector(matsize(f)[1], i, f[i, 1]^f[i, 2])); vector(#f, i, f[i]if(i>1, f[i1])); } \\ Max Alekseyev, May 07 2009


CROSSREFS



KEYWORD

nonn,tabf


AUTHOR



EXTENSIONS



STATUS

approved



