A110893 -id:A110893 - cp's OEIS frontend

A114987 Numbers with a 3-almost prime number of prime divisors (counted with multiplicity).

256, 384, 576, 640, 864, 896, 960, 1296, 1344, 1408, 1440, 1600, 1664, 1944, 2016, 2112, 2160, 2176, 2240, 2400, 2432, 2496, 2916, 2944, 3024, 3136, 3168, 3240, 3264, 3360, 3520, 3600, 3648, 3712, 3744, 3968, 4000, 4096, 4160, 4374, 4416, 4536, 4704

Offset: 1

Jonathan Vos Post, Feb 22 2006

This is the 3-almost prime analog of A063989 "numbers with a prime number of prime divisors (counted with multiplicity)" and A110893 "numbers with a semiprime number of prime divisors (counted with multiplicity)." Below 4096, this is identical to 8-almost primes (A014613). Between 4096 and 6144, this is identical to 8-almost primes. Below 262144 this is identical to the union of 8-almost primes (A014613) and 12-almost primes (A069273). Between 262144 and 393216, this is identical to the union of 8-almost primes and 12-almost primes.

			a(1) = 256 because 256 = 2^8, which has a 3-almost prime (8) number of prime factors with multiplicity.
a(38) = 4096 because 4096 = 2^12, which has a 3-almost prime (12) number of prime factors with multiplicity.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A001222, A014612, A014613, A069273, A069279, A069281.

Select[Range[5000],PrimeOmega[PrimeOmega[#]]==3&] (* Harvey P. Dale, Apr 12 2015 *)

is(n)=bigomega(bigomega(n))==3 \\ Charles R Greathouse IV, Feb 05 2017

a(n) such that A001222(A001222(a(n))) = 3. a(n) such that A001222(a(n)) is an element of A014612. a(n) such that bigomega(a(n)) is an element of A014612. Union[8-almost primes (A014613), 12-almost primes (A069273), 18-almost primes (A069279), 20-almost primes (A069281), 27-almost primes]...

A114985 Numbers whose sum of distinct prime factors is semiprime.

Original entry on oeis.org

14, 21, 26, 28, 30, 33, 38, 46, 52, 56, 57, 60, 62, 63, 69, 70, 74, 76, 85, 90, 92, 93, 94, 98, 99, 102, 104, 105, 106, 112, 120, 124, 129, 133, 134, 140, 145, 147, 148, 150, 152, 166, 171, 174, 177, 178, 180, 182, 184, 188, 189, 190, 195, 196, 204, 205, 207, 208

Offset: 1

Jonathan Vos Post, Feb 22 2006

This is the semiprime analog of A114522 "numbers n such that sum of distinct prime divisors of n is prime." See also A110893 "numbers with a semiprime number of prime divisors (counted with multiplicity)."

			a(1) = 14 because 14 = 2 * 7 and 2 + 7 = 9 = 3^2 is semiprime.
a(2) = 21 because 21 = 3 * 7 and 3 + 7 = 10 = 2 * 5 is semiprime.
a(3) = 26 because 26 = 2 * 13 and 2 + 13 = 15 = 3 * 5 is semiprime.
a(4) = 28 because 28 = 2^2 * 7 and 2 + 7 = 9 = 3^2 is semiprime.
a(5) = 30 because 30 = 2 * 3 * 5 and 2 + 3 + 5 = 10 = 2 * 5 is semiprime.
a(6) = 33 because 33 = 3 * 11 and 3 + 11 = 14 = 2 * 7 is semiprime.
a(7) = 38 because 38 = 2 * 19 and 2 + 19 = 21 = 3 * 7 is semiprime.

Cf. A001358, A008472, A110893, A114522.

with(numtheory): a:=proc(n) local A,s,B: A:=factorset(n): s:=sum(A[j],j=1..nops(A)): B:=factorset(s): if nops(B)=2 and B[1]*B[2]=s or nops(B)=1 and B[1]^2=s then n else fi end: seq(a(n),n=2..250); # Emeric Deutsch, Mar 07 2006

Select[Range[250],PrimeOmega[Total[Transpose[FactorInteger[#]][[1]]]]==2&] (* Harvey P. Dale, May 06 2013 *)

is(n)=bigomega(vecsum(factor(n)[,1]))==2 \\ Charles R Greathouse IV, Sep 14 2015

{k such that A008472(k) is an element of A001358}. {k such that sopf(k) is an element of A001358}. {k = Product(Prime(j)^e_j) such that Sum(Prime(j)) is in A001358}.

Corrected and extended by Emeric Deutsch, Mar 07 2006

cp's OEIS Frontend

A114987 Numbers with a 3-almost prime number of prime divisors (counted with multiplicity).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula