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A232355
Numbers k such that sigma(triangular(k)) = sigma(k)^2.
2
1, 11, 695, 991, 2839, 3707, 9347, 10703, 12847, 27089, 42251, 56419, 74671, 115289, 168739, 191051, 219295, 233729, 280111, 300731, 326899, 353651, 430859, 611799, 642991, 661715, 1035827, 1116607, 1181579, 1234519, 1365491, 1485035, 1777099, 1854671, 1905875
OFFSET
1,2
COMMENTS
Subsequence of A116990. - Michel Marcus, Jun 13 2015
LINKS
EXAMPLE
11 is in the sequence because sigma(11*12/2) = sigma(66) = 144 = 12^2 = sigma(11)^2.
MATHEMATICA
Select[Range@1000000, DivisorSigma[1, #]^2==DivisorSigma[1, (# (# + 1)/2)] &] (* Vincenzo Librandi, Jun 13 2015 *)
PROG
(PARI) isok(n) = sigma(n)^2 == sigma(n*(n+1)/2); \\ Michel Marcus, Nov 23 2013
(Magma) [n: n in [1..7*10^5] | SumOfDivisors(n*(n+1) div 2) eq SumOfDivisors(n)^2]; // Vincenzo Librandi, Jun 13 2015
CROSSREFS
Cf. A000203 (sigma(n): sum of divisors of n), A000217 (triangular(n): = n*(n+1)/2).
Cf. A074285 (sigma(triangular(n))), A072861 (sigma(n)^2).
Cf. A116990 (indices of triangular numbers whose sum of divisors is square).
Sequence in context: A195889 A195519 A218716 * A301732 A028457 A222653
KEYWORD
nonn,changed
AUTHOR
Alex Ratushnyak, Nov 22 2013
EXTENSIONS
More terms from Michel Marcus, Nov 23 2013
STATUS
approved