OFFSET
1,1
EXAMPLE
a(3) = 209 is a term because 209 = 11*19 with Sum_{primes r <= 11} (19 mod r) = (19 mod 2) + (19 mod 3) + (19 mod 5) + (19 mod 7) + (19 mod 11) = 1+1+4+5+8 = 19.
MAPLE
filter:= proc(n) local p, q, r, i;
if numtheory:-bigomega(n) <> 2 then return false fi;
p, q:= (min, max)(numtheory:-factorset(n));
q = add(q mod r, r = select(isprime, [2, seq(i, i=3..p, 2)]))
end proc:
select(filter, [seq(i, i=9..600000, 2)]);
MATHEMATICA
seqQ[n_] := Module[{f = FactorInteger[n], p = 0, q}, If[f[[;; , 2]] == {1, 1}, p = f[[1, 1]]; q = f[[2, 1]]]; If[f[[;; , 2]] == {2}, p = q = f[[1, 1]]]; p > 0 && Sum[Mod[q, r], {r, Select[Range[p], PrimeQ]}] == q]; Select[Range[600000], seqQ] (* Amiram Eldar, Jan 13 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Jan 12 2022
EXTENSIONS
a(10)-a(22) from Amiram Eldar, Jan 13 2022
a(23)-a(30) from Daniel Suteu, May 12 2022
STATUS
approved