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).
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
Keywords
Examples
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.
Links
- Scott R. Shannon, Image of the first 500000 terms. The green line is y = n.
Programs
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Python
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
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