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The total number of factors in unordered factorizations of A025487(n) (Least Prime signatures).
0

%I #12 Dec 06 2020 06:26:29

%S 0,1,3,3,6,8,12,17,10,20,22,34,27,35,46,61,60,54,94,75,107,37,101,123,

%T 86,170,170,176,104,207,230,128,304,356,284,242,386,217,413,192,397,

%U 506,303,434,680,442,512,698,502,703,275,847,832,151,725,818,1244,676,993,1190,1079,1162,399,1654,1311,446,1572,1501,1207,2158,1007,917,1840,1831,1980,2104,1785,1859,1579,556

%N The total number of factors in unordered factorizations of A025487(n) (Least Prime signatures).

%C A025487(n) has a certain number of unordered factorizations with between 1 and A001222(A025487(n)) factors.

%C a(n) counts these factors that are >1. A025487(5) counts 8, 2*4, 2*2*2 with 1+2+3=6=a(5) factors, for example.

%F a(n) = A066637(A025487(n)). [ _R. J. Mathar_, Oct 03 2010]

%e The table of factorizations in A162247 begins:

%e 1

%e 2

%e 3

%e 4 2 2

%e 5

%e 6 2 3

%e 7

%e 8 2 4 2 2 2

%e 9 3 3

%e 10 2 5

%e 11

%e 12 2 6 3 4 2 2 3

%e A025487(n) begins 1 2 4 6 8 12 ...

%e a(n) counts the elements larger than 1 in the A025487(n)-th row of A162247: 0 1 3 3 6 8 ...

%Y Cf. A025487, A162247

%K easy,nonn

%O 1,3

%A _Alford Arnold_, Mar 21 2010

%E a(1) replaced by 0. Sequence extended - _R. J. Mathar_, Oct 03 2010