A357075 Numbers sandwiched between numbers with exactly three distinct prime factors.

131, 139, 155, 169, 181, 221, 229, 239, 259, 265, 281, 307, 309, 311, 341, 349, 365, 371, 373, 379, 407, 409, 439, 441, 443, 469, 475, 491, 493, 505, 517, 519, 521, 529, 531, 533, 551, 559, 573, 581, 589, 599, 601, 611, 617, 619, 637, 643, 645, 664, 671, 679, 681, 683

Offset: 1

Author

Tanya Khovanova, Sep 10 2022

Keywords

• nonn
• easy

Comments

Number k such that both k-1 and k+1 are in A033992.

Examples

			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.
		

Crossrefs

Cf. A033992, A357074, A080569.

Programs

Mathematica

Select[Range[1000],Length[FactorInteger[# + 1]] == 3 && Length[FactorInteger[# - 1]] == 3 &]
Mean/@SequencePosition[Table[If[PrimeNu[n]==3,1,0],{n,700}],{1,,1}] (* _Harvey P. Dale, Jul 06 2025 *)

PARI

is(n)=omega(n-1)==3 && omega(n+1)==3 \\ Charles R Greathouse IV, Sep 11 2022

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

Python

from sympy import factorint
def isA033992(n): return len(factorint(n)) == 3
def ok(n): return isA033992(n-1) and isA033992(n+1)
print([k for k in range(700) if ok(k)]) # Michael S. Branicky, Sep 10 2022