|
| |
|
|
A342246
|
|
Numbers k such that k-1, k and k+1 are all composite with four, five and six (not necessarily distinct) prime factors respectively.
|
|
1
|
|
|
|
11151, 13455, 23375, 26271, 31311, 33776, 36125, 40375, 45495, 46375, 48411, 49049, 49167, 61335, 63125, 74151, 77895, 78111, 78351, 80271, 82575, 83511, 84591, 86031, 87375, 88749, 90207
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
For k=11151 we have 11150 = 2 * 5^2 * 223 which is composite with four prime factors, 11151 = 3^3 * 7 * 59 which is composite with five prime factors and 11152 = 2^4 * 17 * 41 which is composite with six prime factors.
|
|
|
MATHEMATICA
|
SequencePosition[PrimeOmega[Range[100000]], {4, 5, 6}][[;; , 1]]+1 (* Harvey P. Dale, Jul 30 2024 *)
|
|
|
PROG
|
(Sage)
# The following SageMath algorithm will generate all terms up to 100000
L=[]
for n in [1..100000]:
sum1, sum2, sum3 = 0, 0, 0
for f in list(factor(n)):
sum1+=f[1]
for f in list(factor(n+1)):
sum2+=f[1]
for f in list(factor(n+2)):
sum3+=f[1]
if sum1==4 and sum2==5:
if sum3==6:
L.append(n+1)
print(L)
(PARI) for(n=3, 100000, if(bigomega(n-1)==4&&bigomega(n)==5&&bigomega(n+1)==6, print1(n, ", "))) \\ Hugo Pfoertner, Mar 07 2021
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
