

A074851


Numbers k such that k and k+1 both have exactly 2 distinct prime factors.


11



14, 20, 21, 33, 34, 35, 38, 39, 44, 45, 50, 51, 54, 55, 56, 57, 62, 68, 74, 75, 76, 85, 86, 87, 91, 92, 93, 94, 95, 98, 99, 111, 115, 116, 117, 118, 122, 123, 133, 134, 135, 141, 142, 143, 144, 145, 146, 147, 152, 158, 159, 160, 161, 171, 175, 176, 177, 183, 184
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OFFSET

1,1


COMMENTS

Subsequence of A006049.  Michel Marcus, May 06 2016


LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000


FORMULA

a(n) seems to be asymptotic to c*n*log(n)^2 with c=0.13...


EXAMPLE

20=2^2*5 21=3*7 hence 20 is in the sequence.


MATHEMATICA

Flatten[Position[Partition[Table[If[PrimeNu[n]==2, 1, 0], {n, 200}], 2, 1], {1, 1}]] (* Harvey P. Dale, Mar 12 2015 *)


PROG

(PARI) isok(n) = (omega(n) == 2) && (omega(n+1) == 2); \\ Michel Marcus, May 06 2016
(MAGMA) [n: n in [2..200]  #PrimeDivisors(n) eq 2 and #PrimeDivisors(n+1) eq 2]; // Vincenzo Librandi, Dec 05 2018
(GAP) Filtered([1..200], n>[Size(Set(Factors(n))), Size(Set(Factors(n+1)))]=[2, 2]); # Muniru A Asiru, Dec 05 2018
(Python)
import sympy
from sympy.ntheory.factor_ import primenu
for n in range(1, 200):
if primenu(n)==2 and primenu(n+1)==2:
print(n, end=', '); # Stefano Spezia, Dec 05 2018


CROSSREFS

Cf. A006049, A006549.
Analogous sequences for m distinct prime factors: this sequence (m=2), A140077 (m=3), A140078 (m=4), A140079 (m=5).
Cf. A093548.
Equals A255346 \ A321502.
Sequence in context: A006576 A083247 A255346 * A193672 A087678 A144585
Adjacent sequences: A074848 A074849 A074850 * A074852 A074853 A074854


KEYWORD

easy,nonn


AUTHOR

Benoit Cloitre, Sep 10 2002


STATUS

approved



