|
|
A180937
|
|
Sigma-decagonal numbers: numbers n such that sigma(n) is a decagonal number, that is, sigma(n)=4*m^2-3m for some nonnegative integer m.
|
|
1
|
|
|
0, 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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
EXAMPLE
|
sigma(0)=0=4*(0)^2-3*(0) and sigma(1)=1=4*(1)^2-3*(1) so a(0)=0 and 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("C:/temp/sigma-is-decagonal.txt", APPEND);
fprintf(fd, "%d %d\n", n, s);
fclose(fd);
fi;
od; #n
od; #w
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|