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A338565
Number of ordered factorizations of n into decimal palindromes > 1.
3
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
1,4
FORMULA
a(1) = 1; a(n) = Sum_{d|n, d<n} A136522(n/d) * a(d).
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}]
CROSSREFS
Sequence in context: A161904 A360678 A346697 * A323638 A249336 A067004
KEYWORD
nonn,base
AUTHOR
Ilya Gutkovskiy, Nov 02 2020
STATUS
approved