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

1,1

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.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Infinitary Divisor

Example

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.

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 *)

Crossrefs

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

Sequence in context: A329362 A372971 A241604 * A126014 A317420 A256795

Adjacent sequences: A282897 A282898 A282899 * A282901 A282902 A282903

Keyword

nonn

Author

Vladimir Shevelev, Feb 24 2017

Status

approved