A338565 Number of ordered factorizations of n into decimal palindromes > 1.

1, 1, 1, 2, 1, 3, 1, 4, 2, 2, 1, 7, 0, 2, 2, 7, 0, 7, 0, 5, 2, 3, 0, 17, 1, 0, 3, 5, 0, 8, 0, 13, 3, 0, 2, 21, 0, 0, 0, 12, 0, 8, 0, 8, 5, 0, 0, 38, 1, 3, 0, 0, 0, 15, 3, 12, 0, 0, 0, 24, 0, 0, 5, 24, 0, 13, 0, 0, 0, 6, 0, 58, 0, 0, 3, 0, 3, 0, 0, 26, 5, 0, 0, 24, 0, 0, 0, 20, 0, 24

Offset: 1

Author

Ilya Gutkovskiy, Nov 02 2020

Keywords

• nonn
• base

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to palindromes

Crossrefs

Cf. A002113, A136522.

Programs

Maple

ispali:= proc(n) local L;
  L:= convert(n,base,10);
  evalb(L = ListTools:-Reverse(L))
end proc:
N:= 100: # for a(1)..a(N)
Palis:= select(ispali, {$2..N}):
A:= Vector(N):
A[1]:= 1:
for n from 2 to N do
  A[n]:=  add(A[n/d], d= numtheory:-divisors(n) intersect Palis)
od:
convert(A,list); # Robert Israel, Nov 15 2020

Mathematica

a[n_] := If[n == 1, n, Sum[If[(d < n && PalindromeQ[n/d]), a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 1, 90}]

Formula

a(1) = 1; a(n) = Sum_{d|n, dA136522(n/d) * a(d).