A180937 - OEIS

%I #24 Oct 18 2024 10:48:27

%S 1,68,82,290,358,392,445,493,816,880,1024,1136,1150,1224,1275,1296,

%T 1342,1417,1486,1602,1671,1775,1864,2025,2421,2810,3180,3488,3493,

%U 3680,3688,3740,3781,3808,4134,4182,4510,4618,4708,4777,4828,4862,4876,5030,5522,5678

%N Sigma-decagonal numbers: numbers k such that sigma(k) is a decagonal number, that is, sigma(k) = 4*m^2 - 3*m for some nonnegative integer m.

%H Walter A. Kehowski, <a href="/A180937/b180937.txt">Table of n, a(n) for n = 1..1920</a> [Corrected by Sean A. Irvine]

%e sigma(1) = 1 = 4*(1)^2 - 3*(1) so a(1)=1.

%e a(11)=1024 since sigma(1024)=2047 and 2047 = 4*23^2 - 3*23 and 1024 is the 11th such number.

%p with(numtheory);

%p decagonal := proc(n::{nonnegint,symbol}) 4*n^2-3*n end:

%p inv_decagonal :=proc(n::{nonnegint,symbol}) local m; select(z-> type(z,integer) and z>0, [solve(decagonal(m)=n)]) end:

%p N:=map(decagonal,[$1..1000]):

%p L:=[]:

%p for w to 1 do

%p for n from 1 to N[ -1] do

%p s:=sigma(n);

%p if s in N then

%p L:=[op(L),[n,s]];

%p print(n,s);

%p fd:=fopen("sigma-is-decagonal.txt",APPEND);

%p fprintf(fd,"%d %d\n",n,s);

%p fclose(fd);

%p fi;

%p od; #n

%p od; #w

%t Select[Range[10000], IntegerQ[(Sqrt[16*DivisorSigma[1, #] + 9] + 3)/8] &] (* _Paolo Xausa_, Oct 18 2024 *)

%o (PARI) isok(k) = ispolygonal(sigma(k), 10); \\ _Michel Marcus_, May 18 2024

%Y Cf. A000203, A001107.

%K easy,nonn,changed

%O 1,2

%A _Walter Kehowski_, Sep 26 2010

%E Offset changed by _Sean A. Irvine_, May 18 2024