A357074 Numbers sandwiched between a pair of numbers each with exactly two prime factors (counted without multiplicity).

11, 13, 19, 21, 23, 25, 27, 34, 35, 37, 39, 45, 47, 49, 51, 53, 55, 56, 57, 64, 73, 75, 76, 81, 86, 87, 92, 93, 94, 95, 97, 99, 105, 107, 116, 117, 118, 123, 134, 135, 142, 143, 144, 145, 146, 147, 154, 159, 160, 161, 163, 165, 176, 177, 184, 186, 188, 193, 195

Offset: 1

Author

Tanya Khovanova, Sep 10 2022

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A007774.

Programs

Mathematica

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

Python

from sympy import factorint
def isA007774(n): return len(factorint(n)) == 2
def ok(n): return isA007774(n-1) and isA007774(n+1)
print([k for k in range(200) if ok(k)]) # Michael S. Branicky, Sep 10 2022