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A258366 Numbers n representable as x*y + x + y, where x >= y > 1, such that all x's and y's in all representation(s) of n are perfect squares. 0
24, 49, 84, 184, 288, 504, 628, 984, 1284, 1368, 1716, 2004, 2884, 3348, 3384, 3736, 4368, 6484, 6816, 7288, 8004, 9508, 9808, 10200, 11508, 14584, 14836, 15684, 19896, 21348, 21784, 22048, 25048, 25956, 27216, 27384, 35284, 38808, 40500, 40504, 44184, 47988, 49588, 50628 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A subsequence of A254671.

Is 49 the only odd term?

LINKS

Table of n, a(n) for n=1..44.

EXAMPLE

24 = 4*4 + 4 + 4.

49 = 9*4 + 9 + 4, and because this is the only representation, 49 is in the sequence.

129 = 4*25+25+4 = 12*9 + 12 + 9, and because 12 is not a square, 129 is not a term.

PROG

(Python)

def isqrt(a):

    sr = 1L << (long.bit_length(long(a)) >> 1)

    while a < sr*sr:  sr>>=1

    b = sr>>1

    while b:

      s = sr+b

      if a >= s*s:  sr = s

      b>>=1

    return sr

def isSquare(a):

    sr = isqrt(a)

    return (a==sr*sr)

TOP = 100000

a = [0]*TOP

no= [0]*TOP

for y in xrange(2, TOP/2):

  for x in xrange(y, TOP/2):

    k = x*y + x + y

    if k>=TOP: break

    if no[k]==0:

        a[k]=1

        if not (isSquare(x) and isSquare(y)):

            no[k]=1

print [n for n in xrange(TOP) if a[n]>0 and no[n]==0]

CROSSREFS

Cf. A254671, A256073, A000290.

Sequence in context: A044101 A044482 A045294 * A195158 A045279 A042142

Adjacent sequences:  A258363 A258364 A258365 * A258367 A258368 A258369

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, May 27 2015

STATUS

approved

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Last modified September 22 17:11 EDT 2019. Contains 327311 sequences. (Running on oeis4.)