A180937 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.

1, 68, 82, 290, 358, 392, 445, 493, 816, 880, 1024, 1136, 1150, 1224, 1275, 1296, 1342, 1417, 1486, 1602, 1671, 1775, 1864, 2025, 2421, 2810, 3180, 3488, 3493, 3680, 3688, 3740, 3781, 3808, 4134, 4182, 4510, 4618, 4708, 4777, 4828, 4862, 4876, 5030, 5522, 5678

Offset

1,2

Links

Walter A. Kehowski, Table of n, a(n) for n = 1..1920 [Corrected by Sean A. Irvine]

Example

sigma(1) = 1 = 4*(1)^2 - 3*(1) so a(1)=1.
a(11)=1024 since sigma(1024)=2047 and 2047 = 4*23^2 - 3*23 and 1024 is the 11th such number.

Maple

with(numtheory);
decagonal := proc(n::{nonnegint, symbol}) 4*n^2-3*n end:
inv_decagonal :=proc(n::{nonnegint, symbol}) local m; select(z-> type(z, integer) and z>0, [solve(decagonal(m)=n)]) end:
N:=map(decagonal, [$1..1000]):
L:=[]:
for w to 1 do
for n from 1 to N[ -1] do
s:=sigma(n);
if s in N then
L:=[op(L), [n, s]];
print(n, s);
fd:=fopen("sigma-is-decagonal.txt", APPEND);
fprintf(fd, "%d %d\n", n, s);
fclose(fd);
fi;
od; #n
od; #w

Mathematica

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

Prog

(PARI) isok(k) = ispolygonal(sigma(k), 10); \\ Michel Marcus, May 18 2024

Crossrefs

Cf. A000203, A001107.

Sequence in context: A079703 A281235 A097760 * A024881 A039433 A043256

Adjacent sequences: A180934 A180935 A180936 * A180938 A180939 A180940

Keyword

easy,nonn

Author

Walter Kehowski, Sep 26 2010

Extensions

Offset changed by Sean A. Irvine, May 18 2024

Status

approved