%I A055460
%S A055460 0,1,2,2,3,1,2,3,3,1,2,3,4,4,4,4,5,4,5,4,6,6,7,5,5,5,6,5,6,5,6,7,9,7,7,
%T A055460 7,8,8,8,8,9,10,11,10,9,7,8,7,7,8,10,9,10,8,10,12,14,12,13,11,12,12,11,
%U A055460 11,13,12,13,12,12,13,14,13,14,14,15,14,14,11,12,13,13,13,14,16,16,14
%N A055460 Number of distinct prime factors in power power factorization of n! which 
               have odd exponents.
%C A055460 The corresponding prime powers are helpful to compute largest square 
               and square-free part of n!.
%e A055460 n = 100, the exponent set is:{97,48,24,16,9,7,5,5,4,3,3,2,2,2,2,1,1,1,
               1,1,1,1,1,1,1}, 17 odd values arise:{97,9,7,5,5,3,3,1,1,1,1,1,1,1,
               1,1,1}, so a(100) = 17.
%Y A055460 A000142, A007913, A008833.
%Y A055460 Sequence in context: A034968 A054707 A166269 this_sequence A067514 A115323 
               A089282
%Y A055460 Adjacent sequences: A055457 A055458 A055459 this_sequence A055461 A055462 
               A055463
%K A055460 nonn
%O A055460 1,3
%A A055460 Labos E. (labos(AT)ana.sote.hu), Jun 26 2000