A357332 2-adic valuation of A000793(n).

0, 1, 0, 2, 1, 1, 2, 0, 2, 1, 1, 2, 2, 2, 0, 2, 1, 1, 2, 2, 2, 2, 3, 3, 2, 2, 2, 1, 3, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 3, 1, 3, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 3, 1, 3, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 1, 4, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 3, 3, 3

Offset: 1

Author

Jianing Song, Sep 24 2022

Keywords

• nonn

Comments

Is it true that lim_{n->+oo} a(n) = +oo? It seems that the last occurrences of 0, 1, 2, 3, and 4 appear at indices 15, 77, 667, 4535, and 7520. More generally, is it true that lim_{n->+oo} v(A000793(n),p) = +oo for every prime p, where v(k,p) is the p-adic valuation of k?

Examples

			a(15) = 0 since A000793(15) = lcm(3,5,7) = 105 is odd.
a(77) = 1 since A000793(77) = lcm(2,3,5,7,11,13,17,19) = 9699690 is even but not divisible by 4.
		

Links

• Jianing Song, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000793.

Programs

PARI

listn(N) = {
  my(V = vector(N, n, 1));
   forprime (i=2, N,  \\ primes i
      forstep (j=N, i,  -1,
         my( hi = V[j] );
         my( pp = i );  \\ powers of prime i
         while ( pp<=j,  \\ V[] is 1-based
             hi = max(if(j==pp, pp, V[j-pp]*pp), hi);
             pp *= i;
         );
         V[j] = hi;
      );
   );
   vector(N, n, valuation(V[n], 2));
} \\ copied from Joerg Arndt's code for A000793