

A289274


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


3



46, 284, 1633, 149728, 242656, 260495, 298057, 1056752, 9587584, 17706256, 914429696, 985501822, 1074266048, 1484820224, 4241800921, 12147056128, 109548719577, 287291764736, 360499817799
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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 n for which the deficiency of n^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 member 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



