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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). 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS Scott R. Shannon, Image of the first 500000 terms. The green line is y = n. EXAMPLE 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. PROG (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 CROSSREFS Cf. A355648, A355636, A000005, A351001, A352768, A352867, A352774. Sequence in context: A353954 A059041 A129128 * A164922 A205523 A343027 Adjacent sequences: A355644 A355645 A355646 * A355648 A355649 A355650 KEYWORD nonn AUTHOR Scott R. Shannon, Jul 12 2022 STATUS approved

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Last modified December 6 18:28 EST 2022. Contains 358644 sequences. (Running on oeis4.)