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 A357601 For n a power of 2, a(n) = n; otherwise, if 2^m is the greatest power of 2 not exceeding n and if k = n-2^m, then a(n) is the smallest number having d(a(k))+1 divisors which has not occurred earlier (d is the divisor counting function A000005). 1
 1, 2, 3, 4, 5, 9, 25, 8, 7, 49, 121, 6, 169, 10, 14, 16, 11, 289, 361, 15, 529, 21, 22, 81, 841, 26, 27, 625, 33, 2401, 14641, 32, 13, 961, 1369, 34, 1681, 35, 38, 28561, 1849, 39, 46, 83521, 51, 130321, 279841, 12, 2209, 55, 57, 707281, 58, 923521, 1874161, 18 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Based on a similar recursion to that which produces the Doudna sequence, A005940. Conjectured to be permutation of the positive integers in which the primes appear in natural order. LINKS Rémy Sigrist, Table of n, a(n) for n = 1..10000 Rémy Sigrist, PARI program FORMULA a(2^n + 1) = prime(n + 1); n >= 0 A000005(a(n)) = A063787(n). - Rémy Sigrist, Oct 06 2022 EXAMPLE a(9)=7 because k=1, and a(1)=1, which has 1 divisor, so we are looking for the smallest number not yet seen which has 2 divisors. This must be 7 because 2,3,5 have occurred already. MATHEMATICA nn = 70; kk = 2^20; c[_] = False; to = Map[DivisorSigma[0, #] &, Range[kk]^2]; t = DivisorSigma[0, Range[kk]]; Do[Set[{m, k}, {1, n - 2^Floor[Log2[n]]}]; If[k == 0, Set[{a[n], c[n]}, {n, True}], d = 1 + DivisorSigma[0, a[k]]; If[OddQ[d], While[Nand[! c[m^2], to[[m]] == d], m++]; Set[{a[n], c[#]}, {#, True}] &[m^2], While[Nand[! c[m], t[[m]] == d], m++]; Set[{a[n], c[m]}, {m, True}]] ], {n, nn}]; Array[a, nn] (* Michael De Vlieger, Oct 05 2022 *) PROG (PARI) See Links section. CROSSREFS Cf. A000005, A005940, A063787. Sequence in context: A162374 A323289 A355374 * A065885 A274331 A177064 Adjacent sequences: A357598 A357599 A357600 * A357602 A357603 A357604 KEYWORD nonn AUTHOR David James Sycamore, Oct 05 2022 STATUS approved

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Last modified March 5 09:44 EST 2024. Contains 370545 sequences. (Running on oeis4.)