login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A116990 Indices of triangular numbers whose sum of divisors is square. 4
1, 2, 11, 20, 40, 68, 92, 212, 236, 253, 266, 321, 328, 452, 582, 589, 596, 668, 695, 716, 782, 788, 836, 928, 932, 970, 991, 1012, 1065, 1076, 1173, 1264, 1300, 1336, 1388, 1436, 1490, 1549, 1796, 1854, 1927, 1995, 2159, 2228, 2252, 2468, 2545, 2588 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

From Zak Seidov, Oct 19 2010: (Start)

A074285(n) = A000203(A000217(n)) = s^2.

Corresponding values of s begin: 1,2,12,24,42,72,96,216,240,192,240,288,336,456,504, 480,600,672,840,720,720,792,960,930,936,756,992,936,1008,1080,... (are most values of s multiples of 3?).

(End)

LINKS

Zak Seidov, Table of n, a(n) for n = 1..561

FORMULA

n such that A074285(n) is in A000290.

n such that sum( d | A000217(n), d ) is in A000290.

n such that A000203(A000217(n)) is in A000290.

n such that sum( d | n*(n+1)/2, d ) = k^2 for integer k.

EXAMPLE

a(1) = 1 because sigma(1*2/2) = sigma(1) = 1 = 1^2,

a(2) = 2 because sigma(2*3/2) = sigma(3) = 2^2,

a(3) = 11 because sigma(11*12/2) = sigma(66) = 144 = 12^2.

MAPLE

with(numtheory): a:=proc(n) if type(sqrt(sigma(n*(n+1)/2)), integer)=true then n else fi end: seq(a(n), n=0..3100); # Emeric Deutsch, Apr 06 2006

MATHEMATICA

Flatten@ Position[Accumulate[Range@ 2600], n_ /; IntegerQ@ Sqrt@ DivisorSigma[1, n] == True] (* Michael De Vlieger, Mar 17 2015 *)

PROG

(PARI) for(n=1, 1000, if(issquare(sigma(n*(n+1)/2)), print1(n", "))) \\ Zak Seidov, Mar 21 2015

CROSSREFS

See also: A000217 Triangular numbers: a(n) = C(n+1,2) = n(n+1)/2 = 0+1+2+...+n. A074285 Sum of the divisors of n-th triangular number. A083675 Triangular number for which the sum of the proper divisors is also a triangular number. A000203 sigma(n) = sum of divisors of n. Also called sigma_1(n).

Cf. A000203, A000217, A000290, A074285, A083675.

Sequence in context: A279774 A092595 A175927 * A279772 A226416 A146087

Adjacent sequences:  A116987 A116988 A116989 * A116991 A116992 A116993

KEYWORD

easy,nonn,less

AUTHOR

Jonathan Vos Post, Apr 04 2006

EXTENSIONS

More terms from Emeric Deutsch, Apr 06 2006

Incorrect term 0 removed by Michel Marcus, Mar 17 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 23 21:25 EDT 2019. Contains 322388 sequences. (Running on oeis4.)