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A176292 Numbers k such that the prime factorizations of composite(k) and composite(k+1) have the same number of primes (including multiplicities).

%I A176292 #13 Jun 21 2023 12:08:08
%S A176292 1,4,7,10,12,15,17,18,21,22,25,28,29,40,47,53,61,62,64,68,69,72,85,87,
%T A176292 90,91,93,100,102,106,107,110,112,114,116,120,125,130,131,132,133,136,
%U A176292 151,154,155,158,165,166,169,170,179,181,190,191,198,212,221,222,223
%N A176292 Numbers k such that the prime factorizations of composite(k) and composite(k+1) have the same number of primes (including multiplicities).
%H A176292 Harvey P. Dale, <a href="/A176292/b176292.txt">Table of n, a(n) for n = 1..1000</a>
%F A176292 A001222(A002808(a(n))) = A001222(A002808(a(n)+1)).
%p A176292 A001222 := proc(n) numtheory[bigomega](n) ; end proc:
%p A176292 A002808 := proc(n) if n = 1 then return 4; else for a from procname(n-1)+1 do if not isprime(a) then return a; end if; end do; end if; end proc:
%p A176292 for n from 1 to 400 do if A001222(A002808(n)) = A001222(A002808(n+1)) then printf("%d,",n) ; end if; end do: # _R. J. Mathar_, Apr 20 2010
%t A176292 SequencePosition[PrimeOmega/@Select[Range[300],CompositeQ],{x_,x_}][[;;,1]] (* _Harvey P. Dale_, Jun 21 2023 *)
%Y A176292 Cf. A045920, A045939.
%K A176292 nonn
%O A176292 1,2
%A A176292 _Juri-Stepan Gerasimov_, Apr 14 2010
%E A176292 Corrected (86 replaced with 87, 89 removed, many terms after 92 replaced) by _R. J. Mathar_, Apr 20 2010