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

1,4

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?

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A000793.

Sequence in context: A282634 A039980 A306660 * A347367 A194529 A055138

Adjacent sequences: A357329 A357330 A357331 * A357333 A357334 A357335

Keyword

nonn

Author

Jianing Song, Sep 24 2022

Status

approved