A078897 Number of times the greatest prime factor of n is a factor in all numbers <=n; a(1)=1.

1, 1, 1, 3, 1, 2, 1, 7, 4, 2, 1, 5, 1, 2, 3, 15, 1, 8, 1, 4, 3, 2, 1, 10, 6, 2, 13, 4, 1, 7, 1, 31, 3, 2, 5, 17, 1, 2, 3, 9, 1, 6, 1, 4, 10, 2, 1, 22, 8, 12, 3, 4, 1, 26, 5, 9, 3, 2, 1, 14, 1, 2, 10, 63, 5, 6, 1, 4, 3, 11, 1, 34, 1, 2, 18, 4, 7, 6, 1, 19, 40, 2, 1, 13, 5, 2, 3, 8, 1, 21, 7, 4, 3, 2, 5

Offset: 1

Author

Reinhard Zumkeller, Dec 12 2002

Keywords

• nonn

Comments

For n>1: a(n) = 1 iff n is prime.

a(n) = A078896(n) iff n is a prime power (A000961).

Links

• Michel Lagneau, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006530, A078896, A078899.

Programs

Maple

f:= proc(n) local p;
  p:= max(numtheory:-factorset(n));
  add(padic:-ordp(k,p),k=1..n);
end proc:
1, seq(f(n), n=2..1000); # Robert Israel, Dec 23 2014

Mathematica

a[1] = 1; a[n_] := With[{p = FactorInteger[n][[-1, 1]]}, IntegerExponent[ Range[n], p] // Total]; Array[a, 100] (* Jean-François Alcover, Mar 09 2019 *)

PARI

a(n) = if (n==1, 1, my(p = vecmax(factor(n)[,1])); sum(i=1, n, valuation(i, p))); \\ Michel Marcus, Dec 23 2014, Mar 09 2019