login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Numbers sandwiched between a pair of numbers each with exactly two prime factors (counted without multiplicity).
1

%I #9 Sep 11 2022 19:13:28

%S 11,13,19,21,23,25,27,34,35,37,39,45,47,49,51,53,55,56,57,64,73,75,76,

%T 81,86,87,92,93,94,95,97,99,105,107,116,117,118,123,134,135,142,143,

%U 144,145,146,147,154,159,160,161,163,165,176,177,184,186,188,193,195

%N Numbers sandwiched between a pair of numbers each with exactly two prime factors (counted without multiplicity).

%C Number k such that both k-1 and k+1 are in A007774.

%e 11 is sandwiched between 10 = 2*5 and 12 = 2^2*3. Both 10 and 12 have exactly two prime factors. Thus, 11 is in this sequence.

%t Select[Range[1000],Length[FactorInteger[# + 1]] == 2 && Length[FactorInteger[# - 1]] == 2 &]

%o (Python)

%o from sympy import factorint

%o def isA007774(n): return len(factorint(n)) == 2

%o def ok(n): return isA007774(n-1) and isA007774(n+1)

%o print([k for k in range(200) if ok(k)]) # _Michael S. Branicky_, Sep 10 2022

%Y Cf. A007774.

%K nonn

%O 1,1

%A _Tanya Khovanova_, Sep 10 2022