A355636 -id:A355636 - cp's OEIS frontend

A355637 The fixed points of A355636.

1, 3, 6, 55, 58, 189, 372, 1133, 1135, 1374, 1874, 3958, 3959, 3963, 8724, 26492, 29115, 29152, 37628, 39028, 40340, 42183, 42676, 42678, 43731, 44925

Offset: 1

Scott R. Shannon, Jul 11 2022

These are the fixed points in the first 250000 terms of A355636. See that sequence for further details.

Cf. A355636.

A355647 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that has the same number of divisors as the sum a(n-2) + a(n-1).

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 11, 12, 13, 4, 17, 8, 9, 19, 18, 23, 29, 20, 25, 28, 31, 37, 32, 10, 24, 14, 15, 41, 30, 43, 47, 60, 53, 59, 48, 61, 67, 40, 71, 21, 44, 22, 42, 64, 26, 72, 45, 50, 27, 33, 84, 52, 54, 34, 56, 90, 35, 38, 73, 39, 80, 46, 96, 51, 63, 66, 55, 49, 70, 57, 79, 78, 83, 58, 62, 120

Offset: 1

Scott R. Shannon, Jul 12 2022

nonn

In the first 500000 terms the smallest numbers that have not appeared are 15625, 25600, 28561, 36864. It is unknown if these and all other numbers eventually appear. In the same range on eighty-two occasions a(n) equals the sum of the previous two terms, these values begin 3, 5, 17, 64, 90, 73, 120, 144, 192.

See A355648 for the fixed points.

			a(5) = 6 as a(3) + a(4) = 3 + 5 = 8 which has four divisors, and 6 is the smallest unused number that has four divisors.

Scott R. Shannon, Image of the first 500000 terms. The green line is y = n.

Cf. A355648, A355636, A000005, A351001, A352768, A352867, A352774.

from sympy import divisor_count
from itertools import count, islice
def agen():
    anm1, an, mink, seen = 1, 2, 3, {1, 2}
    yield 1
    for n in count(2):
        yield an
        k, target = mink, divisor_count(anm1+an)
        while k in seen or divisor_count(k) != target: k += 1
        while mink in seen: mink += 1
        anm1, an = an, k
        seen.add(an)
print(list(islice(agen(), 76))) # Michael S. Branicky, Jul 26 2022

A355649 a(1) = a(2) = 1; for n > 2, a(n) is the smallest positive number that has the same number of divisors as the sum a(n-2) + a(n-1).

Original entry on oeis.org

1, 1, 2, 2, 4, 6, 6, 12, 12, 24, 36, 60, 60, 120, 180, 180, 360, 360, 720, 840, 840, 1680, 2520, 2520, 5040, 7560, 10080, 10080, 20160, 27720, 27720, 55440, 83160, 110880, 110880, 221760, 332640, 554400, 554400, 1108800, 1441440, 1441440, 2882880, 4324320, 7207200, 7207200, 14414400, 21621600

Offset: 1

Scott R. Shannon, Jul 12 2022

nonn

			a(7) = 6 as a(5) + a(6) = 4 + 6 = 10 which has four divisors, and 6 is the smallest positive number that has four divisors.

Cf. A355636, A000005, A351001, A352768, A352867, A352774.

cp's OEIS Frontend

A355637 The fixed points of A355636.

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A355647 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that has the same number of divisors as the sum a(n-2) + a(n-1).

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A355649 a(1) = a(2) = 1; for n > 2, a(n) is the smallest positive number that has the same number of divisors as the sum a(n-2) + a(n-1).

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