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A070962
a(n) = Card{ k<=n | omega(k)!=omega(n) }, where omega(n) = A001221(n).
2
0, 1, 1, 1, 1, 5, 2, 2, 2, 8, 3, 9, 4, 10, 10, 6, 6, 12, 7, 13, 13, 13, 10, 14, 11, 15, 12, 16, 13, 29, 14, 14, 20, 20, 20, 20, 18, 21, 21, 21, 21, 40, 22, 24, 24, 24, 25, 25, 26, 26, 26, 26, 29, 27, 27, 27, 27, 27, 34, 57, 35, 30, 30, 37, 31, 62, 39, 33, 33, 65, 42, 35, 43, 36
OFFSET
1,6
LINKS
Michael De Vlieger, Scatterplot of a(n), n = 1..2^20.
Eric Weisstein's World of Mathematics, Erdős-Kac theorem
FORMULA
Limit_{n->oo} a(n)/n = 1. This follows from the Erdős-Kac theorem on the distribution of values of omega(n) - see the Weisstein link. - Dean Hickerson, Jan 29 2006
MATHEMATICA
c[_] := 0; Reap[Do[(c[#]++; Sow[n - c[#]]) &@ PrimeNu[n], {n, 120}] ][[-1, 1]] (* Michael De Vlieger, Jun 19 2024 *)
PROG
(PARI) for(n=1, 200, print1(sum(i=1, n, if(omega(n)==omega(i), 0, 1)), ", "))
CROSSREFS
Sequence in context: A286016 A119320 A363252 * A093008 A297827 A198496
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, May 16 2002
EXTENSIONS
Definition corrected by Franklin T. Adams-Watters, Jan 29 2006
STATUS
approved