A358686 Numbers sandwiched between two semiprimes, one of which is a square.

5, 50, 120, 122, 288, 290, 528, 842, 960, 1370, 1680, 1850, 2808, 2810, 4488, 5328, 5330, 6240, 6242, 6888, 6890, 9408, 9410, 11880, 12768, 18770, 22200, 22800, 26568, 27888, 36482, 38808, 39600, 52440, 54290, 58080, 63000, 63002, 69170, 72360, 72362, 73442, 76730, 78960

Offset: 1

Author

Tanya Khovanova, Nov 26 2022

Keywords

• nonn

Comments

Numbers in A124936 but not in A358665.

All numbers except 5 (the first term) are even.

Subsequence of A124936.

Examples

			5 is sandwiched between two semiprimes 4 = 2*2 and 6 = 3*2, one of which is a square. Thus, 5 is in this sequence.
34 is sandwiched between squarefree semiprimes 33 = 3*11 and 35 = 5*7. Thus, 34 is not in this sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..292 (all terms up to 10 million)

Crossrefs

Cf. A001358, A006881, A124936, A358665.

Programs

Mathematica

Select[Range[100000], Total[Transpose[FactorInteger[# - 1]][[2]]] == 2 && Total[Transpose[FactorInteger[# + 1]][[2]]] == 2 && ! (Transpose[FactorInteger[# - 1]][[2]] == {1, 1} && Transpose[FactorInteger[# + 1]][[2]] == {1, 1}) &]
Mean/@Select[SequencePosition[PrimeOmega[Range[80000]],{2,,2}],AnyTrue[Sqrt[#],IntegerQ]&] (* _Harvey P. Dale, Jun 14 2023 *)

Python

from sympy import factorint
from itertools import count, islice
def agen(): # generator of terms
    nxt = []
    yield 5
    for k in count(6, 2):
        prv, nxt = nxt, list(factorint(k+1).values())
        if (prv==[1, 1] and nxt==[2]) or (prv==[2] and nxt==[1, 1]): yield k
print(list(islice(agen(), 44))) # Michael S. Branicky, Nov 26 2022