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A074851
Numbers k such that k and k+1 both have exactly 2 distinct prime factors.
12
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
OFFSET
1,1
COMMENTS
Subsequence of A006049. - Michel Marcus, May 06 2016
LINKS
FORMULA
a(n) seems to be asymptotic to c*n*log(n)^2 with c=0.13...
{k: A001221(k) = A001221(k+1) = 2}. - R. J. Mathar, Jul 18 2023
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
Analogous sequences for m distinct prime factors: this sequence (m=2), A140077 (m=3), A140078 (m=4), A140079 (m=5), A273879 (m=6).
Cf. A093548.
Equals A255346 \ A321502.
Sequence in context: A349262 A083247 A255346 * A193672 A087678 A144585
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Sep 10 2002
STATUS
approved