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A068782 Lesser of two consecutive numbers each divisible by a fourth power. 7
80, 624, 1215, 1376, 2400, 2511, 2672, 3807, 3968, 4374, 5103, 5264, 6399, 6560, 7695, 7856, 8991, 9152, 9375, 10287, 10448, 10624, 11583, 11744, 12879, 13040, 14175, 14336, 14640, 15471, 15632, 16767, 16928, 18063, 18224, 19359, 19375 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The asymptotic density of this sequence is 1 - 2/zeta(4) + Product_{p prime} (1 - 2/p^4) = 0.001856185541538432217... - Amiram Eldar, Feb 16 2021

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

EXAMPLE

80 is a term as 80 and 81 both are divisible by a fourth power, 2^4 and 3^4 respectively.

MATHEMATICA

Select[ Range[2, 25000], Max[ Transpose[ FactorInteger[ # ]] [[2]]] > 3 && Max[ Transpose[ FactorInteger[ # + 1]] [[2]]] > 3 &]

PROG

(PARI) has(n)=vecmax(factor(n)[, 2])>3

is(n)=has(n+1)&&has(n) \\ Charles R Greathouse IV, Dec 19 2018

(PARI) list(lim)=my(v=List(), x=1); forfactored(n=81, lim\1+1, if(vecmax(n[2][, 2])>3, if(x, listput(v, n[1]-1), x=1), x=0)); Vec(v) \\ Charles R Greathouse IV, Dec 19 2018

CROSSREFS

Cf. A068780, A068781, A068140, A068783, A068784, A068785, A046101, A215267.

Sequence in context: A200432 A233351 A107624 * A342188 A255478 A204342

Adjacent sequences:  A068779 A068780 A068781 * A068783 A068784 A068785

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Mar 04 2002

EXTENSIONS

a(0) = 0 removed by Charles R Greathouse IV, Dec 19 2018

STATUS

approved

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Last modified October 26 17:14 EDT 2021. Contains 348268 sequences. (Running on oeis4.)