|
| |
|
|
A256149
|
|
Square numbers n such that sigma(n) is a triangular number.
|
|
4
|
|
|
|
1, 36, 441, 5625, 6084, 407044, 8444836, 17388900, 35070084, 40729924, 57790404, 80138304, 537822481, 588159504, 659821969, 918999225, 1820387556, 2179862721, 2599062361, 5110963081, 28816420516, 36144473689, 46082779561, 55145598561, 147225690000, 163405126756
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
This sequence is the intersection of A000290 and A045746.
|
|
|
LINKS
|
Amiram Eldar, Table of n, a(n) for n = 1..72
|
|
|
EXAMPLE
|
441 is in the sequence because 441 = 21^2 is square number, and sigma(441) = 441 + 147 + 63 + 49 + 21 + 9 + 7 + 3 + 1 = 741 = 38*39/2 is triangular number.
|
|
|
MATHEMATICA
|
t = Accumulate[Range@ 10000]; Select[Range[10000]^2, MemberQ[t, DivisorSigma[1, #]] &] (* Michael De Vlieger, Mar 17 2015 *)
Select[Range[500000]^2, OddQ[Sqrt[8DivisorSigma[1, #]+1]]&] (* Harvey P. Dale, Feb 25 2017 *)
|
|
|
PROG
|
(PARI) {for(i=1, 10^6, n=i*i; if(ispolygonal(sigma(n), 3), print1(n, ", ")))}
|
|
|
CROSSREFS
|
Cf. A000290, A000217, A045746, A083674, A256150, A256151, A256152.
Sequence in context: A178690 A222781 A281403 * A244498 A110693 A104671
Adjacent sequences: A256146 A256147 A256148 * A256150 A256151 A256152
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Antonio Roldán, Mar 16 2015
|
|
|
STATUS
|
approved
|
| |
|
|
