A229321 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).

6, 10, 15, 21, 39, 110, 170, 609, 897, 935, 1265, 1729, 2882, 2915, 12374, 15387, 161833, 411230, 444797, 558830, 842741, 881705, 1091810, 1122501, 1163990, 1342165, 1565565, 1898259, 2763901, 4157605, 4453697, 4675877, 5962835, 6241610, 6809690, 7201599

Offset: 1

Author

Paolo P. Lava, Sep 20 2013

Keywords

• nonn

Comments

Subsequence of A120944.

Examples

			Prime factors of 1265 are 5, 11, 23 and tau(1265) = 8, phi(1265) = 880. 1265 + 880 = 2145 and 2145 / (5 - 8) = -715, 2145 / (11 - 8) = 715, 2145 / (23 - 8) = 143.
		

Crossrefs

Cf. A000005, A000010, A228299-A228302, A229274-A229276, A229322-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 or a[i][1]=tau(n) 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(18)-a(37) from Giovanni Resta, Sep 20 2013

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