A068782 Lesser of two consecutive numbers each divisible by a fourth power.

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

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: A233351 A365887 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