A289274 Numbers k such that the deficiency of k^2 is itself a square > 1.

46, 284, 1633, 149728, 242656, 260495, 298057, 1056752, 9587584, 17706256, 914429696, 985501822, 1074266048, 1484820224, 4241800921, 12147056128, 109548719577, 287291764736, 360499817799

Offset

1,1

Comments

The sequence of square roots of the deficiencies of this sequence is A288144.

The disjoint union of the current sequence with the powers of 2 (A000079) is A289275, the sequence of numbers k for which the deficiency of k^2 is a square (including 1).

Links

Table of n, a(n) for n=1..19.

Example

The deficiency of 46^2 is 2*46^2 - sigma(46^2) = 19^2, so 46 is a term of the sequence.

Maple

issq := n -> evalb(n>1 and issqr(n)):
A033879 := n -> 2*n - numtheory[sigma](n):
isa := n -> issq(A033879(n^2)):
select(isa, [$1..2000]); # Peter Luschny, Jul 25 2017

Prog

(PARI) isok(n) = issquare(d = 2*n^2 - sigma(n^2)) && (d!=1); \\ Michel Marcus, Jul 25 2017

Crossrefs

Cf. A000079, A033879, A288144, A289275.

Sequence in context: A244744 A156841 A086979 * A296402 A077734 A272184

Adjacent sequences: A289271 A289272 A289273 * A289275 A289276 A289277

Keyword

nonn,more

Author

Jens Voß, Jun 30 2017

Extensions

a(10) from Chai Wah Wu, Jul 26 2017

a(11)-a(19) from Giovanni Resta, Jul 27 2017

Status

approved