A229273 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).

6, 10, 15, 22, 78, 138, 273, 483, 3243, 3913, 104377, 477337, 1537627, 1904487, 2508961, 3326829, 3716167, 5148949, 6154017, 6686113, 11521842, 14355679, 16872583, 25165777, 28029883, 31232337, 32403342, 50725419, 57396469, 68815381, 86850249, 98242959

Offset

1,1

Comments

Subsequence of A120944.

Links

Table of n, a(n) for n=1..32.

Example

Prime factors of 273 are 3, 7, 13 and sigma(273) = 448, tau(273) = 8.
273 - 448 = -175 and (-175) / (3 - 8) = 35, (-175) / (7 - 8) = 175, (-175) / (13 - 8) = -35.

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-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(2*10^6);

Crossrefs

Cf. A000005, A000203.

Cf. A228299, A228300, A228301, A228302, A229274, A229275, A229276.

Sequence in context: A093773 A088708 A174872 * A315285 A315286 A315287

Adjacent sequences: A229270 A229271 A229272 * A229274 A229275 A229276

Keyword

nonn

Author

Paolo P. Lava, Sep 19 2013

Extensions

a(20)-a(33) from Giovanni Resta, Sep 20 2013

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

Status

approved