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%I #15 Jan 11 2019 16:54:21
%S 0,0,0,0,0,0,1,1,1,0,2,0,3,0,0,5,5,0,6,0,0,0,9,0,10,0,11,0,12,0,13,13,
%T 1,1,1,1,17,1,1,1,20,0,21,2,2,2,24,2,25,2,2,2,28,2,2,2,2,2,33,0,34,3,
%U 3,36,3,0,38,4,4,0,41,5,42,5,5,5,5,0,47,6,48
%N Number of positive integers less than n with more distinct prime factors than n.
%H Alois P. Heinz, <a href="/A322841/b322841.txt">Table of n, a(n) for n = 1..20000</a>
%e Column n lists the a(n) positive integers less than n with more distinct prime factors than n:
%e 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
%e ---------------------------------------------------------------------
%e 6 6 6 10 12 15 15 18
%e 6 10 14 14 15
%e 6 12 12 14
%e 10 10 12
%e 6 6 10
%e 6
%p b:= proc(n) option remember; nops(numtheory[factorset](n)) end:
%p a:= proc(n) option remember;
%p (t-> add(`if`(b(i)>t, 1, 0), i=1..n-1))(b(n))
%p end:
%p seq(a(n), n=1..100); # _Alois P. Heinz_, Dec 28 2018
%t Table[Length[Select[Range[n],PrimeNu[#]>PrimeNu[n]&]],{n,100}]
%o (PARI) a(n) = my(omegan=omega(n)); sum(k=1, n-1, omega(k) > omegan); \\ _Michel Marcus_, Dec 29 2018
%o (PARI) first(n) = {my(t = 1, pp = 1, res = vector(n)); forprime(p = 2, oo, pp*=p; if(pp > n, v = vector(t); break); t++); for(i = 1, n, o = omega(i); res[i] = v[o+1]; for(j = 1, o, v[j]++)); res} \\ _David A. Corneth_, Dec 29 2018
%Y Positions of zeros are A116998.
%Y Cf. A000010, A000961, A001221, A006049, A058933, A067003, A294277, A302242, A322837, A322838.
%K nonn
%O 1,11
%A _Gus Wiseman_, Dec 28 2018
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