1,2

Every number of the form 2^(j-1)*(2^j - 9), where 2^j - 9 is prime, is a term (cf. A059610). - 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 terms above a(43): 1700388548189538291286016, 5105603016727927767597056, 14752976989200372115199996, 79025520646386734757380096, 85954979333046510417991676. - Max Alekseyev, Oct 20 2025

Max Alekseyev, Table of n, a(n) for n = 1..43 (first 36 terms from Jud McCranie)

q:= k-> nops(map(x-> x mod k, {8, numtheory[sigma](k)}))=1:

select(q, [$1..100000])[]; # Alois P. Heinz, Apr 07 2025

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

Contains subsequence A088833.

Cf. A054024, A045768, A045769, A059610, A088834, A076496.

Sequence in context: A013398 A013493 A166661 * A025632 A038276 A249952

Adjacent sequences: A045767 A045768 A045769 * A045771 A045772 A045773

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

approved