A288144 -id:A288144

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A288145

Square roots of the deficiencies of the squares of A289275.

+10
3

1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 53, 1, 1, 1583, 1, 1, 1, 1, 1, 1, 1, 3509, 6479, 223309, 1, 291205, 1, 1, 65791, 1, 1, 1, 56179, 1, 50039, 1, 1, 1, 1, 1, 3505843, 456456275, 1, 16781311, 5734169, 1, 4144461731, 1, 1, 23461111, 1, 1, 1, 56585278013

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

OFFSET

1,7

COMMENTS

The terms different from 1 in this sequence form sequence A288144.

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..58

CROSSREFS

Cf. A289275, A288144, A289274.

KEYWORD

nonn

AUTHOR

Jens Voß, Jul 01 2017

EXTENSIONS

a(35)-a(54) from Giovanni Resta, Jul 27 2017

STATUS

approved

A289274

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

+10
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 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.

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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