A025730 -id:A025730 - cp's OEIS frontend

A025706 Index of 5^n within sequence of numbers of form 4^i*5^j.

1, 3, 6, 10, 15, 21, 28, 37, 47, 58, 70, 83, 97, 113, 130, 148, 167, 187, 208, 231, 255, 280, 306, 333, 361, 391, 422, 454, 487, 521, 556, 592, 630, 669, 709, 750, 792, 835, 880, 926, 973, 1021, 1070, 1120, 1172, 1225, 1279, 1334, 1390, 1447, 1506, 1566, 1627, 1689

Offset: 0

David W. Wilson

Positions of zeros in A025646. - R. J. Mathar, Jul 06 2025

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Cf. A025646. Differs from A025730 at a(56).

a(n)=my(N=1); n+1+sum(i=1, n, logint(N*=5, 4)); \\ Charles R Greathouse IV, Jan 11 2018

first(n)=my(s, N=1/5); vector(n+1, i, s+=logint(N*=5, 4)+1) \\ Charles R Greathouse IV, Jan 11 2018

Offset corrected by Charles R Greathouse IV, Jan 11 2018

A358038 Partial sums of the cubefree numbers.

Original entry on oeis.org

1, 3, 6, 10, 15, 21, 28, 37, 47, 58, 70, 83, 97, 112, 129, 147, 166, 186, 207, 229, 252, 277, 303, 331, 360, 390, 421, 454, 488, 523, 559, 596, 634, 673, 714, 756, 799, 843, 888, 934, 981, 1030, 1080, 1131, 1183, 1236, 1291, 1348, 1406, 1465, 1525, 1586, 1648, 1711

Offset: 1

Amiram Eldar, Oct 29 2022

nonn

First differs from A025706 and A025730 at n = 14.

The analogous sequence with squarefree numbers is A173143.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Zhu Weiyi, On the cube free number sequences, Smarandache Notions J., Vol. 14 (2004), pp. 199-202.

Cf. A002117, A004709, A173143.

Cf. A025706, A025730.

Accumulate[Select[Range[100], Max[FactorInteger[#][[;; , 2]]] < 3 &]]

a(n) = Sum_{k=1..n} A004709(k).

a(n) = (zeta(3)/2)*n^2 + O(n^(3/2+eps)) (Weiyi, 2004).

Corrected by Amiram Eldar, Jan 02 2024

cp's OEIS Frontend

A025706 Index of 5^n within sequence of numbers of form 4^i*5^j.

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