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.

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

Author

Paolo P. Lava, Aug 20 2013

Keywords

• nonn

Comments

Subsequence of A120944.

Examples

			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.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A000005, A228299, A228300, A228302.

Programs

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);

Extensions

First term deleted by Paolo P. Lava, Sep 23 2013