

A226168


Numbers n such that 1/a + 1/b + 1/c + 1/a*b*c = m /(a+b+c) where a, b and c are the 3 distinct prime divisors of n, and m is a positive integer such that the equation has infinitely many solutions.


0



42, 70, 84, 126, 140, 168, 231, 252, 280, 294, 336, 350, 378, 490, 504, 560, 588, 672, 693, 700, 756, 882, 980, 1008, 1120, 1134, 1176, 1344, 1400, 1512, 1617, 1750, 1764, 1960, 2016, 2058, 2079, 2240, 2268, 2352, 2450, 2541, 2646, 2688, 2800, 3024, 3402, 3430
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OFFSET

1,1


COMMENTS

Subset of A033992.
The value m = 12 is probably unique. We find only 3 primitive values of n: 42 = 2*3*7, 70 = 2*5*7 and 231 = 3*7*11.


LINKS

Table of n, a(n) for n=1..48.
Peter Vandendriessche, Hojoo Lee, Problems in Elementary Number Theory (see problem H67, p. 40). [Via Wayback Machine]


EXAMPLE

42 is in the sequence because the prime divisors of 42 are 2, 3 and 7 => 1/2 + 1/3 + 1/7 + 1/(2*3*7) = 12/(2+3+7) = 1.


MAPLE

with(numtheory): for n from 2 to 3500 do:x:=factorset(n): n1:=nops(x): if n1=3 then x1:=x[1]:x2:=x[2]:x3:=x[3]:s:=1/x1+ 1/x2+ 1/x3+1/(x1*x2*x3): for m from 1 to 500 do:if s=m/(x1+x2+x3) then printf ( "%d %d \n", n, m):else fi:od:fi:od:


CROSSREFS

Cf. A033992.
Sequence in context: A255989 A192274 A291319 * A248430 A340384 A330893
Adjacent sequences: A226165 A226166 A226167 * A226169 A226170 A226171


KEYWORD

nonn


AUTHOR

Michel Lagneau, May 29 2013


STATUS

approved



