login
A372940
Numbers k that divide the k-th Franel number.
1
1, 2, 10, 70, 410, 416, 464, 560, 610, 692, 976, 1840, 2512, 2815, 3712, 4187, 5888, 6026, 7192, 10556, 12064, 14560, 18368, 32704, 33580, 36424, 40016, 41944, 45400, 51940, 58115, 60416, 61544, 62930, 64288, 66976, 80320, 87232, 103247, 110026, 114802, 118400
OFFSET
1,2
COMMENTS
Numbers k such that k | A000172(k).
LINKS
FORMULA
2 is a term since A000172(2) = 10 = 2 * 5 is divisible by 2.
10 is a term since A000172(10) = 38165260 = 10 * 3816526 is divisible by 10.
MATHEMATICA
seq[kmax_] := Module[{f0 = 1, f1 = 2, f2, s = {1}}, Do[f2 = ((7*k^2 - 7*k + 2)*f1 + 8*(k-1)^2*f0)/k^2; If[Divisible[f2, k], AppendTo[s, k]]; f0 = f1; f1 = f2, {k, 2, kmax}]; s]; seq[5000]
PROG
(PARI) lista(kmax) = {my(f0 = 1, f1 = 2, f2); print1("1, "); for(k = 2, kmax, f2 = ((7*k^2 - 7*k + 2)*f1 + 8*(k-1)^2*f0)/k^2; if(!(f2 % k), print1(k, ", ")); f0 = f1; f1 = f2); }
CROSSREFS
Cf. A000172.
Similar sequences: A014847 (Catalan), A016089 (Lucas), A023172 (Fibonacci), A051177 (partition), A232570 (tribonacci), A246692 (Pell), A266969 (Motzkin).
Sequence in context: A293914 A259114 A051575 * A121201 A166076 A354307
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 17 2024
STATUS
approved