A229274 Composite squarefree numbers n such that p+tau(n) divides n-sigma(n), where p are the prime factors of n, tau(n) = A000005(n) and sigma(n) = A000203(n).

51, 93, 177, 219, 303, 471, 597, 681, 723, 807, 849, 933, 1059, 1101, 1227, 1437, 1563, 1689, 1731, 1857, 1941, 1983, 2319, 2361, 2487, 2571, 2823, 2949, 2991, 3117, 3327, 3369, 3453, 3579, 3747, 3831, 3873, 3957, 4083, 4377, 4461, 4629, 4713, 4839, 4881

Offset: 1

Author

Paolo P. Lava, Sep 19 2013

Keywords

• nonn

Comments

Subsequence of A120944.

Examples

			Prime factors of 177 are 3, 59 and sigma(177) = 240 , tau(177) = 4.
177 - 240 = -63 and (-63) / (3 + 4) = -9, (-63) / (59 + 4) = -1.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..999

Crossrefs

Cf. A000005, A000203.

Cf. A228299, A228300, A228301, A228302, A229273, A229275, A229276.

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 then ok:=0; break;
else if not type((n-sigma(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