

A083263


Numbers k such that the difference of the largest and smallest prime factors of k divides k.


2



6, 12, 18, 24, 30, 36, 48, 54, 60, 70, 72, 90, 96, 108, 120, 140, 144, 150, 162, 180, 192, 198, 210, 216, 240, 270, 280, 286, 288, 300, 324, 350, 360, 384, 396, 420, 432, 450, 480, 486, 490, 510, 540, 560, 572, 576, 594, 600, 630, 646, 648, 700, 720, 750, 768
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OFFSET

1,1


LINKS

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


FORMULA

Solutions to x mod (A006530(x)  A020639(x)) = 0.


EXAMPLE

Every number k of the form 2^i * 3^j * m is a term because 3  2 = 1 is always a divisor of k.
Every number k of the form 2 * p * (p+2) * m is a term if p and p+2 form a twin prime pair.
Other terms include some in which the difference d = gpf(k)  lpf(k) > 2 is prime (e.g., 30 = 2*3*5 = 3*10; d = 5  2 = 3) and some in which it is composite (e.g., 8710 = 2*5*13*67 = 65*134; d = 67  2 = 65).
All terms are even.  Jon E. Schoenfield, Jul 10 2018


MATHEMATICA

ffi[x_] := Flatten[FactorInteger[x]]; ba[x_] := Table[Part[ffi[x], 2*w1], {w, 1, lf[x]}]; lf[x_] := Length[FactorInteger[x]]; ma[x_] := Max[ba[x]]; mi[x_] := Min[ba[x]] Do[s=ma[ba[n]]mi[ba[n]]; If[Mod[n, s]==0, Print[{n, ba[n], s}]], {n, 1, 10000}]


CROSSREFS

Cf. A033845, A071141, A006530, A020639.
Sequence in context: A085129 A236240 A242650 * A194385 A043369 A028436
Adjacent sequences: A083260 A083261 A083262 * A083264 A083265 A083266


KEYWORD

nonn


AUTHOR

Labos Elemer, May 12 2003


EXTENSIONS

Edited by Jon E. Schoenfield, Jul 10 2018


STATUS

approved



