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

1,1

Comments

Data provided by Charles R Greathouse IV.

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)

Example

234 = 4*58 + 2, sigma(234) = A000203(234) = 546, 546 mod 234 = 78, and 78 divides 546, so 234 is in the list.

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

Prog

(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
(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
(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

Crossrefs

Cf. A054024, A016825.

Sequence in context: A364825 A245112 A260332 * A364167 A357603 A024486

Adjacent sequences: A254996 A254997 A254998 * A255000 A255001 A255002

Keyword

nonn

Author

J. M. Bergot, Feb 11 2015

Status

approved