A228300 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, 15, 110, 170, 273, 638, 935, 1394, 2093, 2438, 2465, 4823, 5453, 7973, 11978, 16354, 17963, 34918, 43337, 46943, 62491, 64583, 68266, 71603, 72046, 74347, 75361, 85877, 134458, 148291, 155933, 186235, 188071, 201994, 209933, 280891, 307021, 367081

Offset: 1

Author

Paolo P. Lava, Aug 20 2013

Keywords

• nonn

Comments

Subsequence of A120944.

Examples

			Prime factors of 17963 are 11, 23 and 71 while d(17963) = 8. We have that 17963 - 8 = 17955 and 17955 / (11 - 8) =  5985, 17955 / (23 - 8) = 1197 and 17955 / (71 - 8) = 285.
		

Links

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

Crossrefs

Cf. A000005, A228299, A228301, 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