|
|
A361393
|
|
Positive integers k such that 2*omega(k) > bigomega(k).
|
|
6
|
|
|
2, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 26, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 50, 51, 52, 53, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
First differs from A317090 in having 120 and lacking 360.
There are numbers like 1, 120, 168, 180, 252,... which are not in A179983 but in here, and others like 360, 504, 540, 600,... which are in A179983 but not in here. - R. J. Mathar, Mar 21 2023
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
The terms together with their prime indices begin:
2: {1}
3: {2}
5: {3}
6: {1,2}
7: {4}
10: {1,3}
11: {5}
12: {1,1,2}
13: {6}
14: {1,4}
15: {2,3}
17: {7}
18: {1,2,2}
19: {8}
20: {1,1,3}
The prime indices of 120 are {1,1,1,2,3}, with 3 distinct parts and 5 parts, and 2*3 > 5, so 120 is in the sequence.
The prime indices of 360 are {1,1,1,2,2,3}, with 3 distinct parts and 6 parts, and 2*3 is not greater than 6, so 360 is not in the sequence.
|
|
MAPLE
|
isA361393 := proc(n)
if 2*A001221(n) > numtheory[bigomega](n) then
true;
else
false ;
end if:
end proc:
for n from 1 to 100 do
if isA361393(n) then
printf("%d, ", n) ;
end if;
|
|
MATHEMATICA
|
Select[Range[1000], 2*PrimeNu[#]>PrimeOmega[#]&]
|
|
CROSSREFS
|
These partitions are counted by A237365.
A001221 (omega) counts distinct prime factors.
A001222 (bigomega) counts prime factors.
Comparing twice the number of distinct parts to the number of parts:
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|