A046332
Palindromes with exactly 6 prime factors (counted with multiplicity).
Original entry on oeis.org
2772, 2992, 6776, 8008, 21112, 21712, 21912, 23632, 23832, 25452, 25752, 25952, 27472, 28782, 29392, 40104, 40304, 40404, 42024, 42924, 44044, 44144, 44744, 44944, 45954, 46764, 46864, 48984, 53235, 54945, 55755, 59895, 60606, 61216
Offset: 1
Cf.
A046396 (similar but terms must be squarefree),
A373466 (similar, but only distinct prime divisors are counted).
-
N:= 6: # to get all terms of up to N digits
digrev:= proc(n) local L,Ln; L:= convert(n,base,10);Ln:= nops(L);
add(L[i]*10^(Ln-i),i=1..Ln);
end proc:
Res:= NULL:
for d from 2 to N do
if d::even then
m:= d/2;
Res:= Res, select(numtheory:-bigomega=6,
[seq](n*10^m + digrev(n), n=10^(m-1)..10^m-1));
else
m:= (d-1)/2;
Res:= Res, select(numtheory:-bigomega=6,
[seq](seq(n*10^(m+1)+y*10^m+digrev(n), y=0..9), n=10^(m-1)..10^m-1));
fi
od:
map(op,[Res]); # Robert Israel, Dec 23 2014
-
A046332_upto(N, start=1, num_fact=6)={ my(L=List()); while(N >= start = nxt_A002113(start), bigomega(start)==num_fact && listput(L, start)); L} \\ M. F. Hasler, Jun 06 2024
-
from sympy import factorint
def palQgen10(l): # generator of palindromes in base 10 of length <= 2*l
if l > 0:
yield 0
for x in range(1,l+1):
for y in range(10**(x-1),10**x):
s = str(y)
yield int(s+s[-2::-1])
for y in range(10**(x-1),10**x):
s = str(y)
yield int(s+s[::-1])
A046332_list = [x for x in palQgen10(4) if sum(list(factorint(x).values())) == 6]
# Chai Wah Wu, Dec 21 2014
A046396
Palindromes which are the product of 6 distinct primes.
Original entry on oeis.org
222222, 282282, 474474, 555555, 606606, 646646, 969969, 2040402, 2065602, 2206022, 2417142, 2646462, 2673762, 2875782, 3262623, 3309033, 4179714, 4192914, 4356534, 4585854, 4912194, 5021205, 5169615, 5174715, 5578755
Offset: 1
Cf.
A046332 (similar, but for 6 prime factors counted with multiplicity).
Cf.
A074969 (numbers having 6 distinct prime divisors).
-
Select[Range[6*10^6],#==IntegerReverse[#]&&PrimeNu[#]==PrimeOmega[#]==6&] (* The program uses the IntegerReverse function from Mathematica version 10 *) (* Harvey P. Dale, Mar 17 2016 *)
-
A046332_upto(N, start=1, num_fact=6)={ my(L=List()); while(N >= start = nxt_A002113(start), omega(start)==num_fact && issquarefree(start) && listput(L, start)); L} \\ M. F. Hasler, Jun 06 2024
A373465
Palindromes with exactly 5 distinct prime divisors.
Original entry on oeis.org
6006, 8778, 20202, 28182, 40404, 41514, 43134, 50505, 60606, 63336, 66066, 68586, 80808, 83538, 86268, 87978, 111111, 141141, 168861, 171171, 202202, 204402, 209902, 210012, 212212, 219912, 225522, 231132, 232232, 239932, 246642, 249942, 252252, 258852, 262262, 266662, 272272
Offset: 1
a(1) = 6006 = 2 * 3 * 7 * 11 * 13 is a palindrome (A002113) with 5 prime divisors.
a(5) = 40404 = 2^2 * 3 * 7 * 13 * 37 also is a palindrome with 5 prime divisors, although the divisor 2 occurs twice as a factor in the factorization.
Cf.
A046331 (same but counting prime factors with multiplicity),
A046395 (same but squarefree),
A373466 (same with omega = 6),
A373467 (with omega = 7).
-
Select[Range[300000],PalindromeQ[#]&&Length[FactorInteger[#]]==5&] (* James C. McMahon, Jun 08 2024 *)
Select[Range[300000],PalindromeQ[#]&&PrimeNu[#]==5&] (* Harvey P. Dale, Sep 01 2024 *)
-
A373465_upto(N, start=1, num_fact=5)={ my(L=List()); while(N >= start = nxt_A002113(start), omega(start)==num_fact && listput(L, start)); L}
Showing 1-3 of 3 results.
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