cp's OEIS Frontend

A175206 Smallest number k such that omega(k)+ omega(k+1)+ omega(k+2)+ omega(k+3)= n.

%I A175206 #13 Nov 21 2013 13:11:55
%S A175206 1,2,3,9,12,33,75,153,492,987,4179,13803,18444,134043,282489,1013724,
%T A175206 4289592,12582633,57495513,260628717,801621093,3307216989,5313193818,
%U A175206 62909521245,308935340153,611063815284
%N A175206 Smallest number k such that omega(k)+ omega(k+1)+ omega(k+2)+ omega(k+3)= n.
%C A175206 omega(.) = A001221(.) is the number of distinct prime divisors of the argument.
%C A175206 a(29) <= 3169630569180. - _Donovan Johnson_, Sep 17 2011
%D A175206 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 A175206 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.
%e A175206 For n=3, omega(1)+ omega(2)+ omega(3)+ omega(4)= 0 + 1 + 1 + 1 = 3.
%e A175206 For n=4, omega(2)+ omega(3)+ omega(4)+ omega(5)= 1 + 1 + 1 + 1 = 4.
%e A175206 For n=5, omega(3)+ omega(4)+ omega(5)+ omega(6)= 1 + 1 + 1 + 2 = 5.
%e A175206 For n=6, omega(9)+ omega(10)+ omega(11)+ omega(12)= 1 + 2 + 1 + 2 = 6.
%e A175206 For n=7, omega(12)+ omega(13)+ omega(14)+ omega(15)= 2 + 1 + 2 + 2 = 7.
%e A175206 For n=8, omega(33)+ omega(34)+ omega(35)+ omega(36)= 2 + 2 + 2 + 2 = 8.
%e A175206 For n=9, omega(75)+ omega(76)+ omega(77)+ omega(78)= 2 + 2 + 2 + 3 = 9.
%p A175206 with(numtheory):for k from 1 to 20 do : indic:=0: for n from 1 to 1000000000 do :
%p A175206 u1 := nops(factorset(n)): u2 := nops(factorset(n+1)): u3 := nops(factorset(n+2)): u4:= nops(factorset(n+3)):
%p A175206 if u1+u2+u3+u4 = k and indic=0 then print(n): indic:=1: else fi: od: od:
%t A175206 n1=3; nmax=23; omega[k_] := Length[FactorInteger[k]]; Do[om[j] = omega[j], {j, 2, n1+1}]; a[n1]=1; a[n_ /; n>n1] :=  a[n] = (k = a[n-1](* assuming sequence is increasing *); While[k++; Do[om[j] = om[j+1], {j, 1, n1}]; om[n1+1] = omega[k+n1]; Sum[om[j], {j, 1, n1+1}] < n]; k); Table[Print[a[n]]; a[n], {n, n1, nmax}] (* _Jean-François Alcover_,  Sep 12 2011 *)
%Y A175206 Cf. A001222, A001221, A046660, A144494.
%K A175206 nonn
%O A175206 3,2
%A A175206 _Michel Lagneau_, Mar 04 2010
%E A175206 Unspecific references removed, offset corrected, variable names standardized - _R. J. Mathar_, Mar 16 2010
%E A175206 a(24)-a(28) from _Donovan Johnson_, Sep 17 2011