A229275 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).

10778, 16471, 17353, 439453, 1304443, 3719678, 9234253, 17270678, 20512335, 21179143, 50706307, 77292313, 95506557, 103081993, 104707029, 140419077, 240626953, 287947933, 822767689, 982374757, 1608154233, 1918313911, 2219891947, 2471777007, 2632397677

Offset

1,1

Comments

Subsequence of A120944.

Links

Table of n, a(n) for n=1..25.

Example

Prime factors of 10778 are 2, 17, 317 and sigma(10778) = 17172, tau(10778) = 8.
10778 + 17172 = 27950 and 27950 / (2 + 8) = 2795, 27950 / (17 + 8) = 1118, 27950 / (317 + 8) = 86.

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(2*10^6);

Crossrefs

Cf. A000005, A000203, A228299-A228302, A229273, A229274, A229276.

Sequence in context: A023084 A325885 A034231 * A345572 A345828 A151934

Adjacent sequences: A229272 A229273 A229274 * A229276 A229277 A229278

Keyword

nonn

Author

Paolo P. Lava, Sep 19 2013

Extensions

a(4) corrected and a(7)-a(26) by Giovanni Resta, Sep 20 2013

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

Status

approved