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

1,1

Comments

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

Links

Table of n, a(n) for n=1..54.

Example

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.

Mathematica

Select[Range[1000], Length[FactorInteger[# + 1]] == 3 && Length[FactorInteger[# - 1]] == 3 &]

Prog

(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
(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

Crossrefs

Cf. A033992, A357074, A080569.

Sequence in context: A210498 A050671 A095317 * A116519 A139646 A139970

Adjacent sequences: A357072 A357073 A357074 * A357076 A357077 A357078

Keyword

nonn,easy

Author

Tanya Khovanova, Sep 10 2022

Status

approved