login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A353001
Numbers k such that the k-th triangular number mod the sum (with multiplicity) of prime factors of k, and the k-th triangular number mod the sum of divisors of k, are both prime.
2
4, 57, 70, 93, 129, 217, 322, 381, 417, 453, 513, 565, 597, 646, 682, 781, 813, 921, 925, 1057, 1081, 1102, 1137, 1165, 1197, 1261, 1317, 1393, 1405, 1558, 1582, 1641, 1750, 1798, 1846, 1857, 1918, 1929, 2073, 2101, 2110, 2173, 2181, 2305, 2329, 2361, 2482, 2506, 2569, 2577, 2626, 2649, 2653
OFFSET
1,1
COMMENTS
Numbers k such that A232324(k) and A352996(k) are prime.
LINKS
EXAMPLE
a(3) = 70 is a term because 70*71/2 = 2485, A000217(70) = 144, A001414(70) = 14, and both 2485 mod 144 = 37 and 2485 mod 14 = 7 are prime.
MAPLE
filter:= proc(n) local a, b, c, t;
a:= n*(n+1)/2;
b:= add(t[1]*t[2], t=ifactors(n)[2]);
if not isprime(a mod b) then return false fi;
c:= numtheory:-sigma(n);
isprime(a mod c)
end proc:
select(filter, [$2..3000]);
MATHEMATICA
Select[Range[3000], And @@ PrimeQ[Mod[#*(# + 1)/2, {DivisorSigma[1, #], Plus @@ Times @@@ FactorInteger[#]}]] &] (* Amiram Eldar, Apr 15 2022 *)
CROSSREFS
Intersection of A352908 and A352997.
Sequence in context: A092273 A193745 A181437 * A156873 A320977 A071540
KEYWORD
nonn
AUTHOR
Robert Israel, Apr 14 2022
STATUS
approved