A288144 -id:A288144 - cp's OEIS frontend

A288145 Square roots of the deficiencies of the squares of A289275.

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

Offset: 1

Jens Voß, Jul 01 2017

nonn

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

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

Cf. A289275, A288144, A289274.

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

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

Original entry on oeis.org

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

Offset: 1

Jens Voß, Jun 30 2017

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).

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

Cf. A000079, A033879, A288144, A289275.

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

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

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

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

cp's OEIS Frontend

A288145 Square roots of the deficiencies of the squares of A289275.

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

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