cp's OEIS Frontend

A340832 Number of factorizations of n into factors > 1 with odd least factor.

%I A340832 #9 Dec 13 2021 16:15:05
%S A340832 0,0,1,0,1,0,1,0,2,0,1,1,1,0,2,0,1,1,1,0,2,0,1,1,2,0,3,0,1,2,1,0,2,0,
%T A340832 2,2,1,0,2,1,1,1,1,0,4,0,1,2,2,1,2,0,1,2,2,1,2,0,1,3,1,0,4,0,2,1,1,0,
%U A340832 2,2,1,3,1,0,4,0,2,1,1,1,5,0,1,3,2,0,2,0,1,5,2,0,2,0,2,2,1,1,4,1,1,1,1,0,5,0,1,6
%N A340832 Number of factorizations of n into factors > 1 with odd least factor.
%H A340832 Antti Karttunen, <a href="/A340832/b340832.txt">Table of n, a(n) for n = 1..20000</a>
%e A340832 The a(n) factorizations for n = 45, 108, 135, 180, 252:
%e A340832   (45)     (3*36)     (135)      (3*60)     (3*84)
%e A340832   (5*9)    (9*12)     (3*45)     (5*36)     (7*36)
%e A340832   (3*15)   (3*4*9)    (5*27)     (9*20)     (9*28)
%e A340832   (3*3*5)  (3*6*6)    (9*15)     (5*6*6)    (3*3*28)
%e A340832            (3*3*12)   (3*5*9)    (3*3*20)   (3*4*21)
%e A340832            (3*3*3*4)  (3*3*15)   (3*4*15)   (3*6*14)
%e A340832                       (3*3*3*5)  (3*5*12)   (3*7*12)
%e A340832                                  (3*6*10)   (3*3*4*7)
%e A340832                                  (3*3*4*5)
%t A340832 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A340832 Table[Length[Select[facs[n],OddQ@*Min]],{n,100}]
%o A340832 (PARI) A340832(n, m=n, fc=1) = if(1==n, (m%2)&&!fc, my(s=0); fordiv(n, d, if((d>1)&&(d<=m), s += A340832(n/d, d, 0*fc))); (s)); \\ _Antti Karttunen_, Dec 13 2021
%Y A340832 Positions of 0's are A340854.
%Y A340832 Positions of nonzero terms are A340855.
%Y A340832 The version for partitions is A026804.
%Y A340832 Odd-length factorizations are counted by A339890.
%Y A340832 The version looking at greatest factor is A340831.
%Y A340832 - Factorizations -
%Y A340832 A001055 counts factorizations.
%Y A340832 A045778 counts strict factorizations.
%Y A340832 A316439 counts factorizations by product and length.
%Y A340832 A340101 counts factorizations into odd factors, odd-length case A340102.
%Y A340832 A340607 counts factorizations with odd length and greatest factor.
%Y A340832 A340653 counts balanced factorizations.
%Y A340832 - Odd -
%Y A340832 A000009 counts partitions into odd parts.
%Y A340832 A026424 lists numbers with odd Omega.
%Y A340832 A027193 counts partitions of odd length.
%Y A340832 A058695 counts partitions of odd numbers (A300063).
%Y A340832 A066208 lists numbers with odd-indexed prime factors.
%Y A340832 A067659 counts strict partitions of odd length (A030059).
%Y A340832 A174726 counts ordered factorizations of odd length.
%Y A340832 A244991 lists numbers whose greatest prime index is odd.
%Y A340832 A340692 counts partitions of odd rank.
%Y A340832 Cf. A050320, A160786, A340385, A340596, A340599, A340654, A340655, A340931.
%K A340832 nonn
%O A340832 1,9
%A A340832 _Gus Wiseman_, Feb 04 2021
%E A340832 Data section extended up to 108 terms by _Antti Karttunen_, Dec 13 2021