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A228303
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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).
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0
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MAPLE
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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);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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