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 A340102 Number of factorizations of 2n + 1 into an odd number of odd factors > 1. 24
 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,14 LINKS Table of n, a(n) for n=0..86. EXAMPLE The factorizations for 2n + 1 = 135, 225, 315, 405, 675, 1155, 1215: 135 225 315 405 675 1155 1215 3*5*9 5*5*9 5*7*9 5*9*9 3*3*75 3*5*77 3*5*81 3*3*15 3*3*25 3*3*35 3*3*45 3*5*45 3*7*55 3*9*45 3*5*15 3*5*21 3*5*27 3*9*25 5*7*33 5*9*27 3*7*15 3*9*15 5*5*27 3*11*35 9*9*15 3*3*3*3*5 5*9*15 5*11*21 3*15*27 3*15*15 7*11*15 3*3*135 3*3*3*5*5 3*3*3*5*9 3*3*3*3*15 MAPLE g:= proc(n, k, t) option remember; `if`(n>k, 0, t)+ `if`(isprime(n), 0, add(`if`(d>k, 0, g(n/d, d, 1-t)), d=numtheory[divisors](n) minus {1, n})) end: a:= n-> `if`(n=0, 0, g(2*n+1\$2, 1)): seq(a(n), n=0..100); # Alois P. Heinz, Dec 30 2020 MATHEMATICA facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]]; Table[Length[Select[facs[n], OddQ[Length[#]]&&OddQ[Times@@#]&]], {n, 1, 100, 2}]; CROSSREFS The version for partitions is A160786, ranked by A300272. The not necessarily odd-length version is A340101. A000009 counts partitions into odd parts, ranked by A066208. A001055 counts factorizations, with strict case A045778. A027193 counts partitions of odd length, ranked by A026424. A058695 counts partitions of odd numbers, ranked by A300063. A316439 counts factorizations by product and length. Cf. A000700, A002033, A027187, A028260, A074206, A078408, A174726, A236914, A320732, A339846. Sequence in context: A043282 A031226 A031242 * A031260 A360157 A298735 Adjacent sequences: A340099 A340100 A340101 * A340103 A340104 A340105 KEYWORD nonn AUTHOR Gus Wiseman, Dec 30 2020 STATUS approved

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Last modified June 9 11:22 EDT 2023. Contains 363178 sequences. (Running on oeis4.)