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%I #33 Oct 06 2021 12:48:21
%S 1,2,6,45,35,28,22,99,15,20,14,63,33,44,10,75,21,56,26,117,51,68,38,
%T 171,39,52,34,153,57,76,40,55,231,12,46,575,65,78,58,725,85,102,62,
%U 775,95,114,69,805,50,24,87,1015,77,66,60,115,1127,42,74,925,105,18,82,1025,135,36,86,1075,145
%N Variation of the Enots Wolley sequence A336957: earliest infinite sequence of distinct positive integers such that a(n) has a common factor with a(n-1) but not with a(n-2), and has a different number of divisors than a(n-1).
%C This sequence uses the same rules as A336957 except with the additional restriction that a(n) must have a different number of divisors than a(n-1). This leads to the terms showing a greater variation in value. For example in the first 5000 terms the maximum is a(3915) = 228569, compared to a maximum of a(3225) = 11053 for A336957 in the same range. Like A336957 is it likely all positive integers other than the prime-powers eventually appear.
%e a(4) = 45, as a(4) must share a factor with a(3) = 6, have a prime factor not in 6, have no common factor with a(2) = 2, and not have tau(6) = 4 divisors. The smallest positive integer satisfying these conditions is 45. Note that A336957(4) = 15, but 15 has four divisors thus cannot be chosen here.
%Y Cf. A336957, A000005, A098550, A064413.
%K nonn
%O 1,2
%A _Scott R. Shannon_, Sep 27 2021