The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 Table of n, a(n) for n=1..87. 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. Cf. A000041, A000070, A000188, A004526, A030229, A056503, A057567, A082293, A344414. Sequence in context: A335428 A368781 A050377 * A347437 A255231 A363265 Adjacent sequences: A344414 A344415 A344416 * A344418 A344419 A344420 KEYWORD nonn AUTHOR Gus Wiseman, May 22 2021 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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