

A342246


Numbers k such that k1, 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
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OFFSET

1,1


LINKS

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


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.


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(n1)==4&&bigomega(n)==5&&bigomega(n+1)==6, print1(n, ", "))) \\ Hugo Pfoertner, Mar 07 2021


CROSSREFS

Subsequence of A342258.
Cf. A001222, A014613, A014614, A046306.
Sequence in context: A205751 A205473 A250687 * A001727 A190793 A247925
Adjacent sequences: A342243 A342244 A342245 * A342247 A342248 A342249


KEYWORD

nonn


AUTHOR

Sean Lestrange, Mar 07 2021


STATUS

approved



