A145769 Numbers k such that the number of positive divisors of k and the sum of the positive divisors of k are both square numbers.

1, 22, 94, 115, 119, 210, 214, 217, 265, 343, 382, 497, 510, 517, 527, 679, 745, 862, 889, 930, 966, 1155, 1174, 1177, 1207, 1219, 1393, 1416, 1465, 1501, 1566, 1624, 1649, 1672, 1687, 1915, 1942, 2101, 2130, 2159, 2201, 2226, 2346, 2359, 2530, 2618

Offset

1,2

Comments

These might be called square sublime numbers.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

Number of divisors of 94 is 4 = 2^2, sum of divisors of 94 is 144 = 12^2. Hence 94 is in the sequence. [Klaus Brockhaus, Oct 21 2008]

Mathematica

aQ[n_] := AllTrue[{0, 1}, IntegerQ[Sqrt[DivisorSigma[#, n]]] &]; Select[Range[2700], aQ] (* Amiram Eldar, Jul 08 2019 *)

Crossrefs

Cf. A023194.

Cf. A000005 (number of divisors), A000203 (sum of divisors), A000290 (squares). [Klaus Brockhaus, Oct 21 2008]

Sequence in context: A231265 A041944 A230357 * A256152 A159539 A178999

Adjacent sequences: A145766 A145767 A145768 * A145770 A145771 A145772

Keyword

nonn

Author

Howard Berman (howard_berman(AT)hotmail.com), Oct 18 2008

Extensions

Extended by Klaus Brockhaus, Oct 21 2008

Status

approved