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%I #16 Sep 28 2022 11:24:55
%S 131,139,155,169,181,221,229,239,259,265,281,307,309,311,341,349,365,
%T 371,373,379,407,409,439,441,443,469,475,491,493,505,517,519,521,529,
%U 531,533,551,559,573,581,589,599,601,611,617,619,637,643,645,664,671,679,681,683
%N Numbers sandwiched between numbers with exactly three distinct prime factors.
%C Number k such that both k-1 and k+1 are in A033992.
%e 131 is sandwiched between 130 = 2*5*13 and 132 = 2^2*3*11. Both 130 and 132 have exactly three prime factors. Thus, 131 is in this sequence.
%t Select[Range[1000],Length[FactorInteger[# + 1]] == 3 && Length[FactorInteger[# - 1]] == 3 &]
%o (Python)
%o from sympy import factorint
%o def isA033992(n): return len(factorint(n)) == 3
%o def ok(n): return isA033992(n-1) and isA033992(n+1)
%o print([k for k in range(700) if ok(k)]) # _Michael S. Branicky_, Sep 10 2022
%o (PARI) is(n)=omega(n-1)==3 && omega(n+1)==3 \\ _Charles R Greathouse IV_, Sep 11 2022
%o (PARI) list(lim)=my(v=List(),a=3,b,c); forfactored(n=132,lim\1+1, c=#n[2]~; if(c==3 && a==3, listput(v,n[1]-1)); a=b; b=c); Vec(v) \\ _Charles R Greathouse IV_, Sep 28 2022
%Y Cf. A033992, A357074, A080569.
%K nonn,easy
%O 1,1
%A _Tanya Khovanova_, Sep 10 2022
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