A322841 Number of positive integers less than n with more distinct prime factors than n.
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, 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, 3, 36, 3, 0, 38, 4, 4, 0, 41, 5, 42, 5, 5, 5, 5, 0, 47, 6, 48
Offset: 1
Keywords
Examples
Column n lists the a(n) positive integers less than n with more distinct prime factors than n:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
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6 6 6 10 12 15 15 18
6 10 14 14 15
6 12 12 14
10 10 12
6 6 10
6
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..20000
Crossrefs
Programs
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Maple
b:= proc(n) option remember; nops(numtheory[factorset](n)) end: a:= proc(n) option remember; (t-> add(`if`(b(i)>t, 1, 0), i=1..n-1))(b(n)) end: seq(a(n), n=1..100); # Alois P. Heinz, Dec 28 2018 -
Mathematica
Table[Length[Select[Range[n],PrimeNu[#]>PrimeNu[n]&]],{n,100}] -
PARI
a(n) = my(omegan=omega(n)); sum(k=1, n-1, omega(k) > omegan); \\ Michel Marcus, Dec 29 2018
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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