A347984 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).

1, 2, 6, 45, 35, 28, 22, 99, 15, 20, 14, 63, 33, 44, 10, 75, 21, 56, 26, 117, 51, 68, 38, 171, 39, 52, 34, 153, 57, 76, 40, 55, 231, 12, 46, 575, 65, 78, 58, 725, 85, 102, 62, 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

Offset: 1

Author

Scott R. Shannon, Sep 27 2021

Keywords

• nonn

Comments

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.

Examples

			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.
		

Crossrefs

Cf. A336957, A000005, A098550, A064413.