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A045770 Numbers k such that sigma(k) == 8 (mod k).

%I A045770 #56 May 26 2025 00:25:13
%S A045770 1,7,10,49,56,368,836,11096,17816,45356,77744,91388,128768,254012,
%T A045770 388076,2087936,2291936,13174976,29465852,35021696,45335936,120888092,
%U A045770 260378492,381236216,775397948,3381872252,4856970752,6800228816,8589344768,44257207676,114141404156,1461083549696,1471763808896,2199013818368
%N A045770 Numbers k such that sigma(k) == 8 (mod k).
%C A045770 Every number of the form 2^(j-1)*(2^j - 9), where 2^j - 9 is prime, is a term. - _Jon E. Schoenfield_, Jun 02 2019
%C A045770 If m is a term of A045768 with gcd(m,3) = 1 and sigma(m) = 3*q*m + 2 for some integer q, then 3*m is a term of this sequence since sigma(3*m) = 4*q*(3*m) + 8. Some other large terms: 36893488108764397568, 877615520070055755776, 1700388548189538291286016, 85954979333046510417991676, 2081228720695521934665574252544. - _Max Alekseyev_, May 25 2025
%H A045770 Max Alekseyev, <a href="/A045770/b045770.txt">Table of n, a(n) for n = 1..41</a> (first 36 terms from Jud McCranie)
%p A045770 q:= k-> nops(map(x-> x mod k, {8, numtheory[sigma](k)}))=1:
%p A045770 select(q, [$1..100000])[];  # _Alois P. Heinz_, Apr 07 2025
%t A045770 Select[Range[1000000], Mod[DivisorSigma[1, #] - 8, #] == 0 &] (* _Pontus von Brömssen_, Apr 07 2025 *)
%o A045770 (PARI) isok(k) = Mod(sigma(k),k) == 8; \\ _Pontus von Brömssen_, Apr 07 2025
%Y A045770 Cf. A054024, A045768, A045769, A088834, A076496.
%K A045770 nonn
%O A045770 1,2
%A A045770 _Dan Hoey_
%E A045770 a(18)-a(26) from _T. D. Noe_, Apr 06 2011
%E A045770 Initial term 1 added and a(27)-a(31) from _Donovan Johnson_, Mar 01 2012
%E A045770 a(32)-a(34) from _Giovanni Resta_, Apr 02 2014
%E A045770 Term a(2)=7 inserted by _Pontus von Brömssen_, Apr 07 2025