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A357332
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2-adic valuation of A000793(n).
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1
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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
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OFFSET
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1,4
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COMMENTS
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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?
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LINKS
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EXAMPLE
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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.
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PROG
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(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));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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