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.

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

Offset: 1

Author

Sean Lestrange, Mar 07 2021

Keywords

• nonn

Examples

			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.
		

Links

• Dumitru Damian, Table of n, a(n) for n = 1..10456

Crossrefs

Subsequence of A342258.

Cf. A001222, A014613, A014614, A046306.

Programs

Mathematica

SequencePosition[PrimeOmega[Range[100000]],{4,5,6}][[;;,1]]+1 (* Harvey P. Dale, Jul 30 2024 *)

PARI

for(n=3,100000,if(bigomega(n-1)==4&&bigomega(n)==5&&bigomega(n+1)==6,print1(n,", "))) \\ Hugo Pfoertner, Mar 07 2021

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)