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

Author

J. M. Bergot, Feb 11 2015

Keywords

• nonn

Comments

Data provided by Charles R Greathouse IV.

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)

Crossrefs

Cf. A054024, A016825.

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