A175204 Smallest index m such that omega(m) + omega(m+1) + omega(m+2) = n.

1, 2, 4, 10, 20, 68, 154, 644, 2210, 6578, 35308, 92378, 310154, 1042404, 5617820, 35515634, 184055430, 1082950218, 5386096364, 19304763268, 254772473240, 1383442606194

Offset

2,2

Comments

The arithmetic function omega(m) + omega(m+1) + omega(m+2) = Sum_{j=0..2} A001221(m+j) starts 2, 3, 3, 4, 4, 4, 3, 4, 4, 5, 4, 5, 5, 5, 4, 4, 4, 5, 5 (m >= 1).

The sequence is a "first-serve" inverse of this function.

a(24) <= 6127197154440. [Donovan Johnson, Oct 22 2010]

References

J. Peters, A. Lodge and E. J. Ternouth, E. Gifford, Factor Table (n<100000) (British Association Mathematical Tables Vol.V), Burlington House/ Cambridge University Press London 1935.

Links

Table of n, a(n) for n=2..23.

S. Ramanujan, The normal number of prime factors of a number, Quart. J. Math. 48 (1917), 76-92.

Eric Weisstein's World of Mathematics, Distinct Prime Factors.

Example

For n=2, m=1 and omega(1) + omega(2) + omega(3) = 0 + 1 + 1 = 2.
For n=3, m=2 and omega(2) + omega(3) + omega(4) = 1 + 1 + 1 = 3.
For n=4, m=4 and omega(4) + omega(5) + omega(6) = 1 + 1 + 2 = 4.
For n=5, m=10 and omega(10) + omega(11) + omega(12) = 2 + 1 + 2 = 5.
For n=6, m=20 and omega(20) + omega(21) + omega(22) = 2 + 2 + 2 = 6.
For n=7, m=68 and omega(68) + omega(69) + omega(70) = 2 + 2 + 3 = 7.

Maple

with(numtheory): for k from 1 to 20 do :indic:=0: for n from 1 to 2000 do :
s1:= ifactors(n)[2] :u1 :=s1[i][1], i=1..nops(s1):uu1:= nops(s1): s2:= ifactors(n+1)[2] :u2 :=s2[i][1], i=1..nops(s2): uu2:= nops(s2): s3:= ifactors(n+2)[2] :u3 :=s3[i][1], i=1..nops(s3): uu3:= nops(s3): if uu1+uu2+uu3 = k and indic=0 then print(n): indic:=1:else fi:od:od:

Crossrefs

Cf. A001221, A144494.

Sequence in context: A355747 A349430 A129211 * A215533 A128461 A011956

Adjacent sequences: A175201 A175202 A175203 * A175205 A175206 A175207

Keyword

nonn,more

Author

Michel Lagneau, Mar 04 2010

Extensions

Added punctuation to the examples. Corrected and edited by Michel Lagneau, Apr 25 2010

Use of variables adapted to OEIS standards by R. J. Mathar, Oct 12 2010

a(16) corrected and a(19)-a(23) from Donovan Johnson, Oct 22 2010

Status

approved