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A342246 Numbers k such that k-1, k and k+1 are all composite with four, five and six (not necessarily distinct) prime factors respectively.

%I A342246 #27 Jul 30 2024 11:55:12
%S A342246 11151,13455,23375,26271,31311,33776,36125,40375,45495,46375,48411,
%T A342246 49049,49167,61335,63125,74151,77895,78111,78351,80271,82575,83511,
%U A342246 84591,86031,87375,88749,90207
%N A342246 Numbers k such that k-1, k and k+1 are all composite with four, five and six (not necessarily distinct) prime factors respectively.
%H A342246 Dumitru Damian, <a href="/A342246/b342246.txt">Table of n, a(n) for n = 1..10456</a>
%e A342246 For k=11151 we have 11150 = 2 * 5^2 * 223 which is composite with four prime factors, 11151 = 3^3 * 7 * 59 which is composite with five prime factors and 11152 = 2^4 * 17 * 41 which is composite with six prime factors.
%t A342246 SequencePosition[PrimeOmega[Range[100000]],{4,5,6}][[;;,1]]+1 (* _Harvey P. Dale_, Jul 30 2024 *)
%o A342246 (Sage)
%o A342246 # The following SageMath algorithm will generate all terms up to 100000
%o A342246 L=[]
%o A342246 for n in [1..100000]:
%o A342246     sum1, sum2, sum3 = 0,0,0
%o A342246     for f in list(factor(n)):
%o A342246         sum1+=f[1]
%o A342246     for f in list(factor(n+1)):
%o A342246         sum2+=f[1]
%o A342246     for f in list(factor(n+2)):
%o A342246         sum3+=f[1]
%o A342246     if sum1==4 and sum2==5:
%o A342246         if sum3==6:
%o A342246             L.append(n+1)
%o A342246 print(L)
%o A342246 (PARI) for(n=3,100000,if(bigomega(n-1)==4&&bigomega(n)==5&&bigomega(n+1)==6,print1(n,", "))) \\ _Hugo Pfoertner_, Mar 07 2021
%Y A342246 Subsequence of A342258.
%Y A342246 Cf. A001222, A014613, A014614, A046306.
%K A342246 nonn
%O A342246 1,1
%A A342246 _Sean Lestrange_, Mar 07 2021