Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #12 Feb 13 2018 15:16:44
%S 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,
%T 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,
%U 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
%N 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 prime-power p^b(n,p) among the prime-powers (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).
%C Row n contains A001221(n) terms.
%e 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.
%o (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[i-1])); } \\ _Max Alekseyev_, May 07 2009
%Y Cf. A141810, A001221.
%K nonn,tabf
%O 1,2
%A _Leroy Quet_, Aug 03 2008
%E Extended by _Max Alekseyev_, May 07 2009