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A322841 Number of positive integers less than n with more distinct prime factors than n. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,11
LINKS
EXAMPLE
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
---------------------------------------------------------------------
6 6 6 10 12 15 15 18
6 10 14 14 15
6 12 12 14
10 10 12
6 6 10
6
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}]
PROG
(PARI) a(n) = my(omegan=omega(n)); sum(k=1, n-1, omega(k) > omegan); \\ Michel Marcus, Dec 29 2018
(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
CROSSREFS
Positions of zeros are A116998.
Sequence in context: A127640 A113303 A080089 * A291044 A113290 A078442
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 28 2018
STATUS
approved

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Last modified April 12 22:32 EDT 2024. Contains 371639 sequences. (Running on oeis4.)