

A353002


Numbers k such that the kth triangular number mod the sum (with multiplicity) of prime factors of k, and the kth triangular number mod the sum of divisors of k, are the same prime.


0




OFFSET

1,1


LINKS



EXAMPLE

a(1) = 93 is a term because 93*94/2 = 4371, A000217(93) = 128, A001414(93) = 34, and 4371 mod 128 = 4371 mod 34 = 19, which is 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]);
t:= a mod b; if not isprime(t) then return false fi;
c:= numtheory:sigma(n);
a mod c = t
end proc:
select(filter, [$2..2*10^7]);


MATHEMATICA

Select[Range[2*10^6], (r = Mod[#*(# + 1)/2, DivisorSigma[1, #]]) == Mod[#*(# + 1)/2, Plus @@ Times @@@ FactorInteger[#]] && PrimeQ[r] &] (* Amiram Eldar, Apr 15 2022 *)


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



