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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 21 23:29 EST 2019. Contains 320381 sequences. (Running on oeis4.)