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%I #12 Jul 27 2022 13:33:33
%S 1,2,4,3,9,5,25,6,16,8,49,7,121,10,81,12,64,18,625,14,169,11,289,13,
%T 361,15,529,17,841,19,961,21,1369,22,1681,23,1849,26,2209,27,2401,20,
%U 729,24,36,30,100,40,196,42,225,48,256,54,441,56,484,66,676,70,1089,78,1156,80
%N a(1)=1. a(n) = smallest positive integer not occurring earlier in the sequence such that |d(a(n))-d(a(n-1))| = 1, where d(n) is the number of positive divisors of n.
%C Sequence is a permutation of the positive integers.
%C Terms a(65) to a(76) are 1024, 60, 4096, 72, 59049, 84, 531441, 90, 9765625, 96, 244140625, 108. - _Klaus Brockhaus_, Nov 13 2005
%e Among positive integers not among the first 4 terms of the sequence, a(5) = 9 is the lowest such that |d(a(5))-d(a(4))| = |d(9)-d(3)| = |3-2| is 1.
%t Block[{a = {1}, k}, Do[k = 2; While[Nand[FreeQ[a, k], Abs[DivisorSigma[0, k] - DivisorSigma[0, a[[i]]]] == 1], k++]; AppendTo[a, k], {i, 63}]; a] (* _Michael De Vlieger_, Sep 11 2017 *)
%Y Cf. A114107 (inverse), A114108 (number of divisors), A114109 (fixed points), A114110 (records), A114111 (where records occur).
%K nonn
%O 1,2
%A _Leroy Quet_, Nov 10 2005
%E More terms from _Klaus Brockhaus_, Nov 11 2005