cp's OEIS Frontend

A254999 Numbers n of the form 4*k+2 such that (sigma(n) mod n) divides n, where sigma is given by A000203.

%I A254999 #35 Mar 20 2020 09:36:22
%S A254999 2,18,234,650,1890,8190,14850,61110,64890,92070,157950,162162,206910,
%T A254999 258390,365310,383130,558558,702702,711450,743850,822510,916110,
%U A254999 1140750,1561950,1862190,2357550,4977126,5782590
%N A254999 Numbers n of the form 4*k+2 such that (sigma(n) mod n) divides n, where sigma is given by A000203.
%C A254999 Data provided by _Charles R Greathouse IV_.
%H A254999 Chai Wah Wu and Charles R Greathouse IV, <a href="/A254999/b254999.txt">Table of n, a(n) for n = 1..150</a> (first 68 terms from Chai Wah Wu)
%e A254999 234 = 4*58 + 2, sigma(234) = A000203(234) = 546, 546 mod 234 = 78, and 78 divides 546, so 234 is in the list.
%p A254999 for n from 2 by 4 do
%p A254999     m := numtheory[sigma](n) mod n ;
%p A254999     if m <> 0 and modp(n,m) = 0 then
%p A254999         print(n) ;
%p A254999     end if;
%p A254999 end do: # _R. J. Mathar_, Feb 13 2015
%o A254999 (Sage)
%o A254999 [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
%o A254999 (Python)
%o A254999 from sympy import factorint
%o A254999 def sigma_mod(n, m): # computes sigma(n) mod m
%o A254999     y = 1
%o A254999     for p, e in factorint(n).items():
%o A254999         y  = (y*(p**(e + 1) - 1)//(p - 1)) % m
%o A254999     return y
%o A254999 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]
%o A254999 # _Chai Wah Wu_, Mar 01 2015
%o A254999 (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
%Y A254999 Cf. A054024, A016825.
%K A254999 nonn
%O A254999 1,1
%A A254999 _J. M. Bergot_, Feb 11 2015