A291485 - OEIS

%I #24 Mar 27 2024 09:00:05

%S 1,2,3,5,7,8,12,13,15,18,20,24,27,30,31,32,35,38,39,47,48,51,55,56,62,

%T 63,64,79,80,84,90,92,95,96,104,111,116,119,120,128,135,140,142,143,

%U 144,147,152,155,156,159,160,167,168,170,171,175,176,182,184,188,191,192,195,203,207,208

%N Numbers m such that sigma(x) = m*(m+1)/2 has at least one solution.

%C Let b(n) be the smallest k such that sigma(k) is the n-th triangular number, or 0 if no such k exists. For n >= 1, b(n) sequence is 1, 2, 5, 0, 8, 0, 12, 22, 0, 0, 0, 45, 36, 0, 54, 0, 0, 98, 0, 104, 0, 0, 0, 152, 0, 0, 160, 0, 0, 200, ...

%H Amiram Eldar, <a href="/A291485/b291485.txt">Table of n, a(n) for n = 1..10000</a>

%e 15 is a term because sigma(54) = sigma(56) = sigma(87) = sigma(95) = A000217(15).

%p N:= 1000: # to get all terms <= N

%p Sigmas:= {seq(numtheory:-sigma(x),x=1..N*(N+1)/2)}:

%p select(t -> member(t*(t+1)/2, Sigmas), [$1..N]); # _Robert Israel_, Aug 25 2017

%t invT[n_] := (Sqrt[8*n+1]-1)/2; Union@ Select[invT /@ DivisorSigma[1, Range[ 208*209/2]], IntegerQ[#] && # <= 208 &] (* _Giovanni Resta_, Aug 25 2017 *)

%Y Cf. A000203, A000217, A045746.

%K nonn,easy

%O 1,2

%A _Altug Alkan_, Aug 24 2017