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A328338
Numbers whose third-largest divisor is prime.
5
6, 8, 10, 14, 15, 20, 21, 22, 26, 27, 28, 33, 34, 35, 38, 39, 44, 46, 51, 52, 55, 57, 58, 62, 65, 68, 69, 74, 76, 77, 82, 85, 86, 87, 91, 92, 93, 94, 95, 99, 106, 111, 115, 116, 117, 118, 119, 122, 123, 124, 125, 129, 133, 134, 141, 142, 143, 145, 146, 148
OFFSET
1,1
LINKS
EXAMPLE
The sequence of terms together with their divisors begins:
6: {1,2,3,6}
8: {1,2,4,8}
10: {1,2,5,10}
14: {1,2,7,14}
15: {1,3,5,15}
20: {1,2,4,5,10,20}
21: {1,3,7,21}
22: {1,2,11,22}
26: {1,2,13,26}
27: {1,3,9,27}
28: {1,2,4,7,14,28}
33: {1,3,11,33}
34: {1,2,17,34}
35: {1,5,7,35}
38: {1,2,19,38}
39: {1,3,13,39}
44: {1,2,4,11,22,44}
46: {1,2,23,46}
51: {1,3,17,51}
52: {1,2,4,13,26,52}
MAPLE
q:= n-> (l-> nops(l)>2 and isprime(l[-3]))(
sort([numtheory[divisors](n)[]])):
select(q, [$1..200])[]; # Alois P. Heinz, Oct 19 2019
MATHEMATICA
Select[Range[100], Length[Divisors[#]]>2&&PrimeQ[Divisors[#][[-3]]]&]
PROG
(PARI) isA328338(n) = { my(u=numdiv(n)); ((u>2)&&isprime(divisors(n)[u-2])); }; \\ Antti Karttunen, Oct 17 2019
CROSSREFS
A subset of A002808 and superset of A006881.
Numbers whose third-smallest divisor is prime are A119313.
Third-smallest divisor is A292269.
Sequence in context: A331231 A130763 A332269 * A365535 A120497 A036436
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 16 2019
STATUS
approved