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Numbers having a different number of prime factors as their successors (counted with multiplicity).
2

%I #5 Sep 19 2016 09:20:17

%S 1,3,4,5,6,7,8,10,11,12,13,15,16,17,18,19,20,22,23,24,26,28,29,30,31,

%T 32,35,36,37,39,40,41,42,43,45,46,47,48,49,50,51,52,53,54,55,56,58,59,

%U 60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,76,77,78,79,80,81,82,83

%N Numbers having a different number of prime factors as their successors (counted with multiplicity).

%C A077655(a(n))=0; A001222(a(n))<>A001222(a(n)+1).

%e 20=2*2*5 and 20+1=21=3*7: A001222(20)<>A001222(21), therefore 20 is a term (A077655(20)=0).

%t Position[Partition[PrimeOmega[Range[100]],2,1],_?(#[[1]]!=#[[2]]&),{1}, Heads->False]//Flatten (* _Harvey P. Dale_, Sep 19 2016 *)

%Y Cf. A001222, A045920.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Nov 13 2002