A375245 -id:A375245 - cp's OEIS frontend

A375246 Number of biquadratefree numbers <= 10^n.

1, 10, 93, 925, 9240, 92395, 923939, 9239385, 92393839, 923938406, 9239384029, 92393840300, 923938402926, 9239384029211, 92393840292169, 923938402921591, 9239384029215891, 92393840292159004, 923938402921590127, 9239384029215901651, 92393840292159016603

Offset: 0

Chai Wah Wu, Aug 07 2024

nonn

Digits of terms converge to digits of 1/zeta(4) = 90/Pi^4 (A215267).

Chai Wah Wu, Table of n, a(n) for n = 0..39

Cf. A060431, A013662, A046100, A215267, A307430, A375245.

from sympy import mobius, integer_nthroot
def A375246(n): return int(sum(mobius(k)*(10**n//k**4) for k in range(1, integer_nthroot(10**n,4)[0]+1)))

a(n) = A375245(10^n).

A375247 Fluctuations of the number of biquadrate integers not exceeding 10^n.

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 1, 1, -1, 3, 0, 8, 4, -5, 10, 1, -11, -13, -40, -19, -99, 33, -63, 91, 88, 148, -4, -805, 185, 613, -159, -3530, -2419, -5593, -4263, 6633, -553, -3187, -5923, -40742

Offset: 0

Chai Wah Wu, Aug 08 2024

The asymptotic density of biquadrate integers is 90/Pi^4 = 1/zeta(4) = 0.92393840292159... The number of biquadrate integers not exceeding N is approximately N/zeta(4). a(n) gives the difference between this number (A375246) and the linear estimate N/zeta(4) rounded to the nearest integer when N is a power of 10.

Cf. A060431, A013662, A046100, A215267, A307430, A375245, A375246.

a(n) = A375246(10^n)-round(10^n/zeta(4)).

cp's OEIS Frontend

A375246 Number of biquadratefree numbers <= 10^n.

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