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A282900 Least non-infinitary divisor of A162643(n). 3
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 (list; graph; refs; listen; history; text; internal format)
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: A242872 A329362 A241604 * A126014 A317420 A256795

Adjacent sequences:  A282897 A282898 A282899 * A282901 A282902 A282903

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Feb 24 2017

STATUS

approved

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Last modified November 30 18:40 EST 2021. Contains 349424 sequences. (Running on oeis4.)