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

Author

Robert G. Wilson v, Mar 04 2002

Keywords

• nonn

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

Below 9508685764, it suffices to check for n such that either n or n+1 is divisible by p^4 for some p <= 19. - Charles R Greathouse IV, Jul 17 2024

Examples

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

Links

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

Crossrefs

Subsequence of A068140.

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

Programs

Mathematica

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

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

Extensions

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