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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 18 20:53 EDT 2019. Contains 327181 sequences. (Running on oeis4.)