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%I #13 Feb 23 2023 05:11:54
%S 1,2,4,10,20,68,154,644,2210,6578,35308,92378,310154,1042404,5617820,
%T 35515634,184055430,1082950218,5386096364,19304763268,254772473240,
%U 1383442606194
%N Smallest index m such that omega(m) + omega(m+1) + omega(m+2) = n.
%C 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).
%C The sequence is a "first-serve" inverse of this function.
%C a(24) <= 6127197154440. [_Donovan Johnson_, Oct 22 2010]
%D 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.
%H S. Ramanujan, <a href="http://www.imsc.res.in/~rao/ramanujan/CamUnivCpapers/Cpaper35/page1.htm">The normal number of prime factors of a number</a>, Quart. J. Math. 48 (1917), 76-92.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DistinctPrimeFactors.html">Distinct Prime Factors</a>.
%e For n=2, m=1 and omega(1) + omega(2) + omega(3) = 0 + 1 + 1 = 2.
%e For n=3, m=2 and omega(2) + omega(3) + omega(4) = 1 + 1 + 1 = 3.
%e For n=4, m=4 and omega(4) + omega(5) + omega(6) = 1 + 1 + 2 = 4.
%e For n=5, m=10 and omega(10) + omega(11) + omega(12) = 2 + 1 + 2 = 5.
%e For n=6, m=20 and omega(20) + omega(21) + omega(22) = 2 + 2 + 2 = 6.
%e For n=7, m=68 and omega(68) + omega(69) + omega(70) = 2 + 2 + 3 = 7.
%p with(numtheory): for k from 1 to 20 do :indic:=0: for n from 1 to 2000 do :
%p 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:
%Y Cf. A001221, A144494.
%K nonn,more
%O 2,2
%A _Michel Lagneau_, Mar 04 2010
%E Added punctuation to the examples. Corrected and edited by _Michel Lagneau_, Apr 25 2010
%E Use of variables adapted to OEIS standards by _R. J. Mathar_, Oct 12 2010
%E a(16) corrected and a(19)-a(23) from _Donovan Johnson_, Oct 22 2010
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