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A228301
Composite squarefree numbers n such that p-d(n) divides n+d(n), where p are the prime factors of n and d(n) the number of divisors of n.
5
6, 10, 14, 15, 35, 70, 154, 190, 322, 385, 442, 595, 682, 2737, 3619, 14986, 15314, 19019, 24817, 26767, 33626, 78387, 85034, 130169, 155363, 166934, 189727, 214107, 225029, 238901, 243217, 285934, 381547, 395219, 415679, 417989, 455609, 466193, 544918
OFFSET
1,1
COMMENTS
Subsequence of A120944.
LINKS
EXAMPLE
Prime factors of 19019 are 7, 11, 13 and 19 while d(19019) = 16. We have that 19019 + 16 = 19035 and 19035 / (7 - 16) = -2115, 19035 / (11 - 16) = -3807, 19035 / (13 - 16) = -6345 and 19035 / (19 - 16) = 6345.
MAPLE
with (numtheory); P:=proc(q) local a, b, c, i, ok, p, n;
for n from 2 to q do if not isprime(n) then a:=ifactors(n)[2]; ok:=1;
for i from 1 to nops(a) do if a[i][2]>1 or a[i][1]=tau(n) then ok:=0; break;
else if not type((n+tau(n))/(a[i][1]-tau(n)), integer) then ok:=0; break; fi; fi; od; if ok=1 then print(n); fi; fi; od; end: P(10^6);
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Aug 20 2013
EXTENSIONS
First term deleted by Paolo P. Lava, Sep 23 2013
STATUS
approved