A046338 -id:A046338 - cp's OEIS frontend

A046337 Odd numbers with an even number of prime factors (counted with multiplicity).

1, 9, 15, 21, 25, 33, 35, 39, 49, 51, 55, 57, 65, 69, 77, 81, 85, 87, 91, 93, 95, 111, 115, 119, 121, 123, 129, 133, 135, 141, 143, 145, 155, 159, 161, 169, 177, 183, 185, 187, 189, 201, 203, 205, 209, 213, 215, 217, 219, 221, 225, 235, 237, 247, 249, 253, 259

Offset: 1

Patrick De Geest, Jun 15 1998

nonn

John Cerkan, Table of n, a(n) for n = 1..10000

Intersection of A005408 and A028260.
Setwise difference A005408 \ A067019.
Setwise difference A028260 \ A063745.
Union of A359161 and A359163.
Union of A327862 and A360110.
Subsequence of A345452, of A356312 and of A359371.
Positions of positive terms in A166698, positions of even terms in A327858 and A356299.
Subsequences: A002557, A046315 (odd semiprimes), A056913, A359596, A359607, A359608 (without its term 2).
Cf. A000035, A008836, A046338, A046470, A353557 (characteristic function), A358777.
Cf. also A036349, A297845.

Select[Range[1,301,2],EvenQ[PrimeOmega[#]]&] (* Harvey P. Dale, Jul 25 2011 *)

lista(nn) = {forstep(n=1, nn, 2, if (bigomega(n) % 2 == 0, print1(n, ", ")));} \\ Michel Marcus, Jul 04 2015

{k | A000035(k) > 0 and A008836(k) > 0}. - Antti Karttunen, Jan 13 2023

A046328 Palindromes with exactly 2 prime factors (counted with multiplicity).

Original entry on oeis.org

4, 6, 9, 22, 33, 55, 77, 111, 121, 141, 161, 202, 262, 303, 323, 393, 454, 505, 515, 535, 545, 565, 626, 707, 717, 737, 767, 818, 838, 878, 898, 939, 949, 959, 979, 989, 1111, 1441, 1661, 1991, 3113, 3223, 3443, 3883, 7117, 7447, 7997, 9119, 9229, 9449, 10001

Offset: 1

Patrick De Geest, Jun 15 1998

			111 is a palindrome and 111 = 3*37. 3 and 37 are primes.

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 2000 terms from Zak Seidov, terms a(2001)-a(2816) from Michael De Vlieger)

Cf. A046315, A046408, A108505.

Subsequence of A001358 and A046338.

fQ[n_] := Block[{id = IntegerDigits[n]}, Plus @@ Last /@ FactorInteger[n] == 2 && id == Reverse[id]]; Select[ Range[ 10000], fQ[ # ] &] (* Robert G. Wilson v, Jun 06 2005 *)
Select[Range[10002], Reverse[x = IntegerDigits[#]] == x && PrimeOmega[#] == 2 &] (* Jayanta Basu, Jun 23 2013 *)
Select[Range[11000],PalindromeQ[#]&&PrimeOmega[#]==2&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 30 2018 *)

ispal(n) = my(d=digits(n));d == Vecrev(d) \\ A002113
for(k=1,1e4,if(ispal(k)&&bigomega(k)==2, print1(k, ", "))) \\ Alexandru Petrescu, Jul 07 2022

from sympy import factorint
from itertools import product
def ispal(n): s = str(n); return s == s[::-1]
def pals(d, base=10): # all d-digit palindromes
    digits = "".join(str(i) for i in range(base))
    for p in product(digits, repeat=d//2):
        if d > 1 and p[0] == "0": continue
        left = "".join(p); right = left[::-1]
        for mid in [[""], digits][d%2]: yield int(left + mid + right)
def ok(pal): return sum(factorint(pal).values()) == 2
print(list(filter(ok, (p for d in range(1, 6) for p in pals(d) if ok(p))))) # Michael S. Branicky, Aug 14 2022

cp's OEIS Frontend

A046337 Odd numbers with an even number of prime factors (counted with multiplicity).

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