A080193 -id:A080193 - cp's OEIS frontend

A104355 Number of trailing zeros in decimal representation of A104350(n).

0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

Offset: 1

Reinhard Zumkeller, Mar 06 2005

Amiram Eldar, Table of n, a(n) for n = 1..10000
David A. Corneth, PARI link
Reinhard Zumkeller, Products of largest prime factors of numbers <= n.

Cf. A000079, A027868, A080193, A104350, A104356, A122840.

IntegerExponent[FoldList[Times, Array[FactorInteger[#][[-1, 1]] &, 100]], 10] (* Amiram Eldar, Apr 08 2024 *)

gpf(n) = {my(p = factor(n)[, 1]); p[#p];}
a(n) = valuation(prod(k = 2, n, gpf(k)), 10); \\ Amiram Eldar, Apr 08 2024

\\ See link. David A. Corneth, Apr 08 2024

a(A104356(n)) = n and a(m) < n for m < A104356(n);

a(n) = A122840(A104350(n)). - Reinhard Zumkeller, Mar 10 2013

A301506 Number of integers less than or equal to n whose largest prime factor is 5.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11

Offset: 0

Ralph-Joseph Tatt, Mar 22 2018

nonn

a(n) increases when n has the form 2^a*3^b*5^c, with a,b >= 0 and c > 0.

A distinct sequence can be generated for each prime number; this sequence is for the prime number 5. For an example using another prime number see A301461.

			a(15) = a(2^0 * 3^1 * 5^1); 5 is the largest prime factor, so a(15) exceeds the previous term by 1. For a(16) = a(2^4), there is no increase from the previous term.

Robert Israel, Table of n, a(n) for n = 0..10000

Cf. A080193.

Cf. A301461.

clear;clc;
prime = 5;
limit = 10000;
largest_divisor = ones(1,limit+1);
for k = 0:limit
    f = factor(k);
    largest_divisor(k+1) = f(end);
end
for i = 1:limit+1
    FQN(i) = sum(largest_divisor(1:i)==prime);
end
output = [0:limit;FQN]'

N:= 100: # for a(0)..a(N)
L:= sort([seq(seq(seq(2^a*3^b*5^c, c=1..floor(log[5](N/(2^a*3^b)))),
  b = 0..floor(log[3](N/2^a))), a = 0 .. floor(log[2](N)))]):
V:= Array(0..N):
V[L]:= 1:
ListTools:-PartialSums(convert(V,list)); # Robert Israel, Sep 22 2020

Accumulate@ Array[Boole[FactorInteger[#][[-1, 1]] == 5] &, 80, 0] (* Michael De Vlieger, Apr 21 2018 *)

cp's OEIS Frontend

A104355 Number of trailing zeros in decimal representation of A104350(n).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Formula

A301506 Number of integers less than or equal to n whose largest prime factor is 5.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

MATLAB

Maple

Mathematica