Search: id:A035310
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%I A035310
%S A035310 1,4,12,47,170,750,3255,16010,81199,448156
%N A035310 Let f(n) = number of ways to factor n = A001055(n); a(n) = sum of f(k) 
               over all terms k in A025487 that have n factors.
%C A035310 Ways of partitioning an n-multiset with multiplicities some partition 
               of n.
%e A035310 a(3) = 12 because there are 3 terms in A025487 with 3 factors, namely 
               8, 12, 30; and f(8)=3, f(12)=4, f(30)=5 and 3+4+5 = 12.
%Y A035310 Cf. A025487, A000041, A000110, A035098, A080688.
%Y A035310 Sequence A035341 counts the ordered cases. Tables A093936 and A095705 
               distribute the values; e.g. 81199 = 30 + 536 + 3036 + 6181 + 10726 
               + 11913 + 14548 + 13082 + 21147.
%Y A035310 Cf. A035341 A093936 A095705.
%Y A035310 Sequence in context: A000775 A149374 A149375 this_sequence A022016 A151441 
               A032380
%Y A035310 Adjacent sequences: A035307 A035308 A035309 this_sequence A035311 A035312 
               A035313
%K A035310 nonn,nice
%O A035310 1,2
%A A035310 Alford Arnold (Alford1940(AT)aol.com)
%E A035310 More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
%E A035310 81199 from Alford Arnold (Alford1940(AT)aol.com), Mar 04 2008
%E A035310 a(10) from Alford Arnold (Alford1940(AT)aol.com), Mar 31 2008
%E A035310 a(10) corrected. Alford Arnold (Alford1940(AT)aol.com), Aug 07 2008

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