login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A254999 Numbers n of the form 4*k+2 such that (sigma(n) mod n) divides n, where sigma is given by A000203. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A227934 A245112 A260332 * A024486 A052635 A259270

Adjacent sequences:  A254996 A254997 A254998 * A255000 A255001 A255002

KEYWORD

nonn

AUTHOR

J. M. Bergot, Feb 11 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 21 21:51 EDT 2021. Contains 348155 sequences. (Running on oeis4.)