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A254999
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Numbers n of the form 4*k+2 such that (sigma(n) mod n) divides n, where sigma is given by A000203.
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1
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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
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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234 = 4*58 + 2, sigma(234) = A000203(234) = 546, 546 mod 234 = 78, and 78 divides 546, so 234 is in the list.
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MAPLE
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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;
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PROG
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(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]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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