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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

Table of n, a(n) for n=1..29.

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

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