A282900 Least non-infinitary divisor of A162643(n).

2, 3, 2, 2, 3, 2, 5, 2, 4, 2, 2, 3, 2, 7, 5, 2, 2, 3, 2, 2, 3, 5, 2, 2, 3, 2, 3, 2, 4, 7, 3, 2, 2, 2, 2, 3, 11, 2, 3, 2, 2, 2, 7, 2, 5, 3, 2, 4, 3, 2, 13, 3, 2, 5, 2, 2, 2, 2, 2, 3

Offset: 1

Author

Vladimir Shevelev, Feb 24 2017

Keywords

• nonn

Comments

Let n=q_1*...*q_t, where q_i are distinct increasing terms of A050376. This representation is unique (for n=1 the product is empty). Every subproduct is an infinitary divisor of n. All numbers having at least one non-infinitary divisor form A162643.

Examples

			For n=60=3*4*5, no subproduct is 2,6,10,30. They are all non-infinitary divisors of 60. Since 60=A162643(17) then a(17) = 2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Infinitary Divisor

Crossrefs

Cf. A000005, A036537, A037445, A050376, A162643.

Programs

Mathematica

Map[First@ Complement[Divisors@ #, If[# == 1, {1}, Sort@ Flatten@ Outer[Times, Sequence @@ (FactorInteger[#] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]]] &, Select[Range@ 198, ! IntegerQ@ Log2@ DivisorSigma[0, #] &]] (* Michael De Vlieger, Feb 24 2017, after Paul Abbott at A077609 *)