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

 

Logo
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

%I #24 Jan 16 2018 02:38:27

%S 105,805,4147,6745,37411,55309,68593,252433,281177,560101,754261,

%T 774397,1698391,4052093,10102441,15571753,26117137,26238073,26449711,

%U 28949077,29261497,46273753,58499101,64611121,72766297,112871581,133506361,198410339,502541443

%N 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).

%C 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.

%C Subsequence of A120944.

%e 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.

%p with (numtheory); P:=proc(q) local a,b,i,ok,n;

%p for n from 2 to q do if not isprime(n) then a:=ifactors(n)[2]; ok:=1;

%p b:=add(a[i][1]*a[i][2],i=1..nops(a));

%p for i from 1 to nops(a) do if a[i][2]>1 or a[i][1]=b then ok:=0; break;

%p else if not type((n+b)/(a[i][1]-b),integer) then ok:=0; break; fi; fi; od;

%p if ok=1 then print(n); fi; fi; od; end: P(10^6);

%Y Cf. A001414, A120944.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Aug 20 2013

%E First term deleted by _Paolo P. Lava_, Sep 23 2013

%E a(16)-a(29) from _Donovan Johnson_, Nov 14 2013

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 11:44 EDT 2024. Contains 371241 sequences. (Running on oeis4.)