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Numbers k such that the k-th triangular number == 1 mod the integer log of k.
2

%I #11 Apr 20 2022 00:08:05

%S 2,6,12,21,33,45,52,63,136,162,201,205,208,225,245,253,301,304,344,

%T 441,494,531,550,637,697,720,742,806,901,910,918,1078,1233,1242,1274,

%U 1333,1376,1540,1566,1573,1625,1680,1695,1792,1863,1909,2025,2041,2107,2295,2466,2497,2774,2896,2926,2965

%N Numbers k such that the k-th triangular number == 1 mod the integer log of k.

%C Numbers k such that A000217(k) == 1 (mod A001414(k)).

%H Robert Israel, <a href="/A352990/b352990.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 12 = 2*2*3 is a term because 12*13/2 = 78 == 1 (mod 2+2+3 = 7).

%p filter:= proc(n) local t; (n*(n+1)/2) mod add(t[1]*t[2],t=ifactors(n)[2]) = 1 end proc:

%p select(filter, [$2..3000]);

%t Select[Range[3000], Mod[#*(# + 1)/2, Plus @@ Times @@@ FactorInteger[#]] == 1 &] (* _Amiram Eldar_, Apr 14 2022 *)

%Y Cf. A000217, A001414, A352989.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Apr 13 2022