A372940 Numbers k that divide the k-th Franel number.

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

Amiram Eldar, Table of n, a(n) for n = 1..345

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

Adjacent sequences: A372937 A372938 A372939 * A372941 A372942 A372943

Keyword

nonn

Author

Amiram Eldar, May 17 2024

Status

approved