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

1, 7, 10, 49, 56, 368, 836, 11096, 17816, 45356, 77744, 91388, 128768, 254012, 388076, 2087936, 2291936, 13174976, 29465852, 35021696, 45335936, 120888092, 260378492, 381236216, 775397948, 3381872252, 4856970752, 6800228816, 8589344768, 44257207676, 114141404156, 1461083549696, 1471763808896, 2199013818368

Offset: 1

Author

Dan Hoey

Keywords

• nonn

Comments

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

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

Links

• Max Alekseyev, Table of n, a(n) for n = 1..41 (first 36 terms from Jud McCranie)

Crossrefs

Cf. A054024, A045768, A045769, A088834, A076496.

Programs

Maple

q:= k-> nops(map(x-> x mod k, {8, numtheory[sigma](k)}))=1:
select(q, [$1..100000])[];  # Alois P. Heinz, Apr 07 2025

Mathematica

Select[Range[1000000], Mod[DivisorSigma[1, #] - 8, #] == 0 &] (* Pontus von Brömssen, Apr 07 2025 *)

PARI

isok(k) = Mod(sigma(k),k) == 8; \\ Pontus von Brömssen, Apr 07 2025

Extensions

a(18)-a(26) from T. D. Noe, Apr 06 2011

Initial term 1 added and a(27)-a(31) from Donovan Johnson, Mar 01 2012

a(32)-a(34) from Giovanni Resta, Apr 02 2014

Term a(2)=7 inserted by Pontus von Brömssen, Apr 07 2025