The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 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 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 A330893 A305153 Adjacent sequences:  A226165 A226166 A226167 * A226169 A226170 A226171 KEYWORD nonn AUTHOR Michel Lagneau, May 29 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 27 22:11 EST 2020. Contains 338684 sequences. (Running on oeis4.)