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A122401 Subsequence of A074139 omitting values derived from partitions with a part of size 1.

%I A122401 #8 Aug 28 2018 13:56:24
%S A122401 1,3,4,5,9,6,12,7,15,16,27,8,18,20,36,9,21,24,25,45,48,81,10,24,28,30,
%T A122401 54,60,64,108,11,27,32,35,63,36,72,75,80,135,144,243,12,30,36,40,72,
%U A122401 42,84,90,96,162,100,180,192,324,13,33,40,45,81,48,96,49,105,112,189,108,120,216,125,225,240,405,256,432,729,14,36,44,50,90,54
%N A122401 Subsequence of A074139 omitting values derived from partitions with a part of size 1.
%C A122401 When viewed as a table, row sums are given by sequence A079274.
%C A122401 Corresponds to members of A036035 which are also powerful numbers (A001694).
%e A122401 The two cyclic partitions of five are 5 and 3+2 yielding (5+1)=6 and (3+1)*(2+1) = 4*3 = 12
%e A122401 The array begins
%e A122401 1
%e A122401 (empty)
%e A122401 3
%e A122401 4
%e A122401 5 9
%e A122401 6 12
%e A122401 7 15 16 27
%e A122401 8 18 20 36
%p A122401 A122401_row := proc(n)
%p A122401     local e, a,L;
%p A122401     L := [] ;
%p A122401     for e in ListTools[Reverse](partition(n)) do
%p A122401         if member(1,e) then
%p A122401             ;
%p A122401         else
%p A122401             a := 1;
%p A122401             for p in e do
%p A122401                 a := a*(p+1) ;
%p A122401             end do:
%p A122401             L := [op(L),a] ;
%p A122401         end if;
%p A122401     end do:
%p A122401     L ;
%p A122401 end proc:
%p A122401 seq(A122401_row(i), i=0..15); # _R. J. Mathar_, Aug 28 2018
%Y A122401 Cf. A122172 A079274 A122402, A316532.
%K A122401 easy,nonn,tabf
%O A122401 0,2
%A A122401 _Alford Arnold_, Sep 01 2006
%E A122401 Extended by _R. J. Mathar_, Aug 28 2018