A228302 Composite squarefree numbers n such that p+d(n) divides n-d(n) for all prime factors p of n, where d(n) is the number of divisors of n.

4958, 51653, 55583, 1251574, 4909102, 5430797, 5785073, 6096931, 13892243, 14058781, 14809517, 16699426, 27391073, 32426566, 32673383, 38669686, 43459682, 44762461, 53638783, 69836866, 74975761, 75226313, 85607461, 96973703, 105139141, 122864065

Offset: 1

Author

Paolo P. Lava, Aug 20 2013

Keywords

• nonn

Comments

Subsequence of A120944.

Examples

			Prime factors of 51653 are 7, 47 and 157 while d(51653) = 8. We have that 51653 - 8 = 51645 and 51645 / (7 + 8) =  3443, 51645 / (47 + 8) = 939 and 51645 / (157 + 8) = 313.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000005, A228299-A228301.

Programs

Maple

with(numtheory);  P:=proc(q) local a,i,ok,p,n;
for n from 1 to q do if not isprime(n) and issqrfree(n) then
a:=ifactors(n)[2]; ok:=1; for i from 1 to nops(a) do
if not type((n-tau(n))/(a[i][1]+tau(n)),integer) then ok:=0; break; fi; od;
if ok=1 then print(n); fi; fi; od; end: P(10^9);

Extensions

More terms from Michel Marcus, Sep 21 2013

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