A085779 -id:A085779 - cp's OEIS frontend

A215011 a(n) = least k>0 such that triangular(n) divides Fibonacci(k).

1, 4, 12, 15, 20, 8, 24, 12, 60, 10, 60, 84, 56, 40, 60, 18, 36, 36, 90, 120, 40, 120, 24, 300, 175, 252, 72, 168, 140, 60, 60, 60, 180, 360, 120, 228, 342, 252, 420, 60, 40, 88, 660, 60, 120, 48, 48, 168, 1400, 900, 252, 189, 108, 180, 120, 72, 252, 406, 1740

Offset: 1

Alex Ratushnyak, Aug 08 2012

nonn

Triangular(n)=n*(n+1)/2 is the n-th triangular number.

			Triangular(2)=3, least k>0 such that 3 divides Fibonacci(k) is k=4, so a(2)=4.

Cf. A085779 (least k such that triangular(n) divides k!).
Cf. A001177 (least k such that n divides Fibonacci(k)).
Cf. A132632 (least k such that n^2 divides Fibonacci(k)).
Cf. A132633 (least k such that n^3 divides Fibonacci(k)).
Cf. A215453 (least k such that n^n divides Fibonacci(k)).
Cf. A214528 (least k such that n! divides Fibonacci(k)).
Cf. A000217, A000045.

lk[n_]:=Module[{k=1,t=(n(n+1))/2},While[Mod[Fibonacci[k],t]!=0,k++];k]; Array[lk,60] (* Harvey P. Dale, Jun 19 2021 *)

TOP = 333
prpr = y = 0
prev = k = 1
res = [-1]*TOP
while y

A215454 a(n) = least positive k such that n^2 divides k!

Original entry on oeis.org

1, 4, 6, 6, 10, 6, 14, 8, 9, 10, 22, 6, 26, 14, 10, 10, 34, 9, 38, 10, 14, 22, 46, 8, 20, 26, 15, 14, 58, 10, 62, 12, 22, 34, 14, 9, 74, 38, 26, 10, 82, 14, 86, 22, 10, 46, 94, 10, 28, 20, 34, 26, 106, 15, 22, 14, 38, 58, 118, 10, 122, 62, 14, 16, 26, 22, 134, 34

Offset: 1

Alex Ratushnyak, Aug 11 2012

nonn

Indices n such that a(n)=n: 1 followed by A074845.

			a(12): least positive k such that 144 divides k! is k=6, 6!=720. So a(12)=6.

Cf. A002034 (least k such that n divides k!).
Cf. A085779 (least k such that triangular(n) divides k!).
Cf. A093896 (least positive k such that n^n divides k!).

Module[{nn=200,f},f=Range[nn]!;Position[f,#]&/@Table[SelectFirst[ f, Divisible[ #,n^2]&],{n,nn}]]//Flatten (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 11 2018 *)

TOP = 77
ii = [0]*TOP
for i in range(1, TOP):
    ii[i] = i*i
f = k = y = 1
res = [-1]*TOP
while y

cp's OEIS Frontend

A215011 a(n) = least k>0 such that triangular(n) divides Fibonacci(k).

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