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A111972 a(n) = Max(omega(k): 1<=k<=n), where omega(n) = A001221(n), the number of distinct prime factors of n. 4
0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

This sequence has the same relationship to A001221 as A000523 has to A001222. Also, for n>=1, n-1 occurs as A002110(n)-A002110(n-1) consecutive terms beginning with term a(A002110(n-1)), where A002110 is the primorials; i.e. the frequencies of occurrence are the first differences (1,4,24,180,...) of the primorials.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..65536

EXAMPLE

a(7)=2 because omega(1)=0, omega(2)=omega(3)=omega(4)=omega(5)=omega(7)=1 and omega(6)=2 (as 6=2*3), so 2 is the maximum.

MAPLE

a:= proc(n) option remember; `if`(n=0, 0,

      max(a(n-1), nops(ifactors(n)[2])))

    end:

seq(a(n), n=1..105);  # Alois P. Heinz, Aug 19 2021

CROSSREFS

Cf. A001221 (omega(n)), A002110 (primorials), A000523 (Log_2(n) rounded down), A001222 (Omega(n), also known as bigomega(n)).

Sequence in context: A204551 A292563 A211661 * A073458 A194698 A105519

Adjacent sequences:  A111969 A111970 A111971 * A111973 A111974 A111975

KEYWORD

nonn

AUTHOR

Rick L. Shepherd, Aug 24 2005

STATUS

approved

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Last modified December 1 13:00 EST 2021. Contains 349429 sequences. (Running on oeis4.)