A229276 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, 66, 145, 231, 435, 1221, 11571, 99093, 105502, 292434, 449854, 585429, 643858, 968014, 1372494, 1787091, 1939434, 4659114, 5524014, 5654334, 6250371, 6974007, 19495374, 19821714, 28488039, 34701369, 46183893, 81133734, 213352233, 230140869

Offset

1,1

Comments

Subsequence of A120944.

Links

Kevin P. Thompson, Table of n, a(n) for n = 1..62

Example

Prime factors of 435 are 3, 5, 29 and sigma(435) = 720, tau(435) = 8.
435 + 720 = 1155 and 1155 / (3 - 8) = -231, 1155 / (5 - 8) = -385, 1155 / (29 - 8) = 55.

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, A228299-A228302, A229273-A229275.

Sequence in context: A048017 A332392 A048078 * A319035 A117309 A228300

Adjacent sequences: A229273 A229274 A229275 * A229277 A229278 A229279

Keyword

nonn

Author

Paolo P. Lava, Sep 19 2013

Extensions

a(21)-a(33) from Giovanni Resta, Sep 20 2013

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

Status

approved