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A344417 Number of palindromic factorizations of n. 2
1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1, 4, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 4, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 7, 1, 1, 1, 2, 1, 1, 1, 5, 1, 1, 2, 2, 1, 1, 1, 4, 4, 1, 1, 2, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
A palindrome is a sequence that is the same whether it is read forward or in reverse. A palindromic factorization of n is a finite multiset of positive integers > 1 with product n that can be permuted into a palindrome.
LINKS
FORMULA
a(2^n) = A025065(n).
a(n) = A057567(A000188(n)). - Andrew Howroyd, May 22 2021
EXAMPLE
The palindromic factorizations for n = 2, 4, 16, 36, 64, 144:
(2) (4) (16) (36) (64) (144)
(2*2) (4*4) (6*6) (8*8) (12*12)
(2*2*4) (2*2*9) (4*4*4) (4*4*9)
(2*2*2*2) (3*3*4) (2*2*16) (4*6*6)
(2*2*3*3) (2*2*4*4) (2*2*36)
(2*2*2*2*4) (3*3*16)
(2*2*2*2*2*2) (2*2*6*6)
(3*3*4*4)
(2*2*2*2*9)
(2*2*3*3*4)
(2*2*2*2*3*3)
MATHEMATICA
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
palQ[y_]:=Select[Permutations[y], #==Reverse[#]&]!={};
Table[Length[Select[facs[n], palQ]], {n, 50}]
CROSSREFS
Positions of 1's are A005117.
The case of palindromic compositions is A016116.
The additive version (palindromic partitions) is A025065.
The case of palindromic prime signature is A242414.
The case of palindromic plane trees is A319436.
A001055 counts factorizations.
A229153 ranks non-palindromic partitions.
A265640 ranks palindromic partitions.
Sequence in context: A335428 A368781 A050377 * A347437 A255231 A363265
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 22 2021
STATUS
approved

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Last modified May 23 02:40 EDT 2024. Contains 372758 sequences. (Running on oeis4.)