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 A353002 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 the same prime. 0
 93, 2653, 30433, 1922113, 15421122, 28776673, 240409057, 611393953, 2713190397, 5413336381 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..10. 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 Cf. A000217, A001414, A232324, A352996, A353001. Sequence in context: A250373 A250374 A146125 * A017809 A017756 A246991 Adjacent sequences: A352999 A353000 A353001 * A353003 A353004 A353005 KEYWORD nonn,more AUTHOR J. M. Bergot and Robert Israel, Apr 15 2022 EXTENSIONS a(8) from Amiram Eldar, Apr 15 2022 a(9)-a(10) from Daniel Suteu, May 12 2022 STATUS approved

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Last modified December 2 16:47 EST 2023. Contains 367525 sequences. (Running on oeis4.)