A254999 Numbers n of the form 4*k+2 such that (sigma(n) mod n) divides n, where sigma is given by A000203.
2, 18, 234, 650, 1890, 8190, 14850, 61110, 64890, 92070, 157950, 162162, 206910, 258390, 365310, 383130, 558558, 702702, 711450, 743850, 822510, 916110, 1140750, 1561950, 1862190, 2357550, 4977126, 5782590
Offset: 1
Keywords
Examples
234 = 4*58 + 2, sigma(234) = A000203(234) = 546, 546 mod 234 = 78, and 78 divides 546, so 234 is in the list.
Links
- Chai Wah Wu and Charles R Greathouse IV, Table of n, a(n) for n = 1..150 (first 68 terms from Chai Wah Wu)
Programs
-
Maple
for n from 2 by 4 do m := numtheory[sigma](n) mod n ; if m <> 0 and modp(n,m) = 0 then print(n) ; end if; end do: # R. J. Mathar, Feb 13 2015 -
PARI
select(n->my(s=sigma(n)%n); s && n%s==0, vector(1000,n,4*n-2)) \\ Charles R Greathouse IV, Mar 17 2015
-
Python
from sympy import factorint def sigma_mod(n, m): # computes sigma(n) mod m y = 1 for p, e in factorint(n).items(): y = (y*(p**(e + 1) - 1)//(p - 1)) % m return y A254999_list = [n for n,m in ((4*k+2, sigma_mod(4*k+2,4*k+2)) for k in range(10**6)) if m and not n % m] # Chai Wah Wu, Mar 01 2015 -
Sage
[4*k+2 for k in [0..600000] if sigma(4*k+2)%(4*k+2)!=0 and (4*k+2)%(sigma(4*k+2)%(4*k+2))==0] # Tom Edgar, Feb 12 2015
Comments