OFFSET
1,27
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..20000
EXAMPLE
The a(n) factorizations for n = 27, 84, 108, 180, 252, 360, 432:
27 2*6*7 2*6*9 4*5*9 4*7*9 5*8*9 6*8*9
3*3*3 3*4*7 3*4*9 2*2*45 6*6*7 2*4*45 2*8*27
2*2*21 2*2*27 2*6*15 2*2*63 3*8*15 4*4*27
2*2*3*3*3 3*4*15 2*6*21 4*6*15 2*2*2*6*9
2*2*3*3*5 3*4*21 2*12*15 2*2*3*4*9
2*2*3*3*7 2*2*2*5*9 2*2*2*2*27
2*3*3*4*5 2*2*2*2*3*3*3
2*2*2*3*15
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[Max@@#]&]], {n, 100}]
PROG
(PARI) A340607(n, m=n, k=0, grodd=0) = if(1==n, k, my(s=0); fordiv(n, d, if((d>1)&&(d<=m)&&(grodd||(d%2)), s += A340607(n/d, d, 1-k, bitor(1, grodd)))); (s)); \\ Antti Karttunen, Dec 13 2021
CROSSREFS
Note: Heinz numbers are given in parentheses below.
The case of odd length only is A339890.
The case of all odd factors is A340102.
The version for partitions is A340385.
The version for prime indices is A340386.
The case of odd maximum only is A340831.
A316439 counts factorizations by sum and length.
A340101 counts factorizations (into odd factors = of odd numbers).
A340832 counts factorizations whose least part is odd.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 25 2021
EXTENSIONS
Data section extended up to 108 terms by Antti Karttunen, Dec 13 2021
STATUS
approved