A229322 Composite squarefree numbers n such that p + tau(n) divides n + phi(n), where p are the prime factors of n, tau(n) = A000005(n) and phi(n) = A000010(n).

72285, 82218, 1612671, 52371129, 511130199, 2111850465, 4789685289, 8884216243, 8916435021, 9863075721, 15364177629, 28243714821, 99459827349

Offset: 1

Author

Paolo P. Lava, Sep 20 2013

Keywords

• nonn

Comments

a(15) > 10^11. - Giovanni Resta, Sep 20 2013

Subsequence of A120944.

Examples

			Prime factors of 82218 are 2, 3, 71, 193 and tau(82218) = 16, phi(82218) = 26680. 82218 + 26680 = 109098 and  109098 / (2 + 16) = 6061, 109098 / (3 + 16) = 5742, 109098 / (71 + 16) = 1254, 109098 / (193 + 16) = 522.
		

Crossrefs

Cf. A000005, A000010, A228299-A228302, A229274-A229276, A229321, A229323, A229324.

Programs

Maple

with (numtheory); P:=proc(q) global 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 then ok:=0; break;
else if not type((n+phi(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(6*10^9);

Extensions

a(4)-a(14) from Giovanni Resta, Sep 20 2013

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