

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



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
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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



