The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A228303 Composite squarefree numbers n such that each p-sopfr(n) divides n+sopfr(n), where p runs through the prime factors of n, and where sopfr(n) is the sum of the prime factors of n (A001414). 0
 105, 805, 4147, 6745, 37411, 55309, 68593, 252433, 281177, 560101, 754261, 774397, 1698391, 4052093, 10102441, 15571753, 26117137, 26238073, 26449711, 28949077, 29261497, 46273753, 58499101, 64611121, 72766297, 112871581, 133506361, 198410339, 502541443 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Up to n=10^7 no solution for p+sopfr(n) | n+sopfr(n) and p+sopfr(n) | n-sopfr(n) while p-sopfr(n) | n-sopfr(n) is satisfied by 8216395 and 8880415. Subsequence of A120944. LINKS EXAMPLE Prime factors of 37411 are 11, 19 and 179 while sopfr(37411) = 209. We have that 37411 + 209 = 37620 and 37620 / (11 - 209) = -190, 37620 / (19 - 209) = -198 and 37620 / (179 - 209) = -1254. MAPLE with (numtheory); P:=proc(q) local a, b, i, ok, n; for n from 2 to q do if not isprime(n) then a:=ifactors(n)[2]; ok:=1; b:=add(a[i][1]*a[i][2], i=1..nops(a)); for i from 1 to nops(a) do if a[i][2]>1 or a[i][1]=b then ok:=0; break; else if not type((n+b)/(a[i][1]-b), integer) then ok:=0; break; fi; fi; od; if ok=1 then print(n); fi; fi; od; end: P(10^6); CROSSREFS Cf. A001414, A120944. Sequence in context: A133767 A166816 A166798 * A033593 A297542 A266105 Adjacent sequences: A228300 A228301 A228302 * A228304 A228305 A228306 KEYWORD nonn AUTHOR Paolo P. Lava, Aug 20 2013 EXTENSIONS First term deleted by Paolo P. Lava, Sep 23 2013 a(16)-a(29) from Donovan Johnson, Nov 14 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 9 10:28 EST 2022. Contains 358700 sequences. (Running on oeis4.)