

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
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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



