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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 Alois P. Heinz, Table of n, a(n) for n = 1..20000 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. Cf. A000010, A000961, A001221, A006049, A058933, A067003, A294277, A302242, A322837, A322838. Sequence in context: A127640 A113303 A080089 * A291044 A113290 A078442 Adjacent sequences: A322838 A322839 A322840 * A322842 A322843 A322844 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.)