A303216
A(n,k) is the n-th Fibonacci number with exactly k prime factors (counted with multiplicity); square array A(n,k), n>=1, k>=1, read by antidiagonals.
Original entry on oeis.org
2, 21, 3, 8, 34, 5, 6765, 610, 55, 13, 2584, 196418, 987, 377, 89, 144, 701408733, 317811, 10946, 4181, 233, 832040, 102334155, 1134903170, 2178309, 75025, 17711, 1597, 86267571272, 267914296, 12586269025, 365435296162, 32951280099, 3524578, 121393, 28657
Offset: 1
Square array A(n,k) begins:
2, 21, 8, 6765, 2584, 144, ...
3, 34, 610, 196418, 701408733, 102334155, ...
5, 55, 987, 317811, 1134903170, 12586269025, ...
13, 377, 10946, 2178309, 365435296162, 10610209857723, ...
89, 4181, 75025, 32951280099, 6557470319842, 2111485077978050, ...
233, 17711, 3524578, 139583862445, 72723460248141, 7540113804746346429, ...
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F:= combinat[fibonacci]: with(numtheory):
A:= proc() local h, p, q; p, q:= proc() [] end, 2;
proc(n, k)
while nops(p(k))
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A[n_, k_] := Module[{F = Fibonacci, h, p, q = 2}, p[_] = {}; While[ Length[p[k]] < n, q = q+1; h = PrimeOmega[F[q]]; p[h] = Append[p[h], F[q]]]; p[k][[n]]];
Table[Table[A[n, 1+d-n], {n, 1, d}], {d, 1, 10}] // Flatten (* Jean-François Alcover, Feb 05 2021, after Alois P. Heinz *)
A072396
Index of smallest Fibonacci number with n prime factors when counted with multiplicity.
Original entry on oeis.org
3, 8, 6, 20, 18, 12, 30, 54, 24, 36, 138, 48, 84, 72, 108, 96, 210, 120, 276, 168, 216, 252, 288, 240, 336, 570, 384, 420, 360, 576, 480, 540, 504, 660, 600, 672, 990, 720, 792, 840, 1152, 1140
Offset: 1
a(3) = 6 since the 6th Fibonacci number 8 has 3 prime factors.
A359876
a(n) is the smallest tribonacci number (A000073) with exactly n prime factors (counted with multiplicity).
Original entry on oeis.org
1, 2, 4, 44, 24, 5768, 504, 10562230626642, 3136, 7046319384, 615693474, 53798080, 4680045560037375, 35574238430251050319992, 4659412488735286161146176, 23523635785731871586396890786299881280, 79932289960699059086717998848
Offset: 0
a(5) = 5768, because 5768 is a tribonacci number with 5 prime factors (counted with multiplicity) {2, 2, 2, 7, 103} and this is the smallest such number.
A359877
a(n) is the smallest tetranacci number (A000078) with exactly n prime factors (counted with multiplicity).
Original entry on oeis.org
1, 2, 4, 8, 56, 108, 5536, 28074040, 39648, 147312, 18566888967365603514688, 9966792788887776, 2775641472, 2505471397838180985096739296, 1445523368993397560000765219760086502994234237205516083525719052320, 44092571484448511101335177770183225655413760
Offset: 0
a(6) = 5536, because 5536 is a tetranacci number with 6 prime factors (counted with multiplicity) {2, 2, 2, 2, 2, 173} and this is the smallest such number.
A359880
a(n) is the smallest Fibonacci n-step number with exactly n prime factors (counted with multiplicity).
Original entry on oeis.org
21, 44, 56, 120, 1936, 2000, 2035872, 32512, 265816832, 523008, 8565824256, 67047424, 134156288, 1073463296, 35176050802688, 8589344768, 562914520154112, 18013762856812544, 144112508021833728, 2305819919496904704, 1099509006336, 137438822400
Offset: 2
a(3) = 44, because 44 is a tribonacci number with 3 prime factors (counted with multiplicity) {2, 2, 11} and this is the smallest such number.
Showing 1-5 of 5 results.
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