A328338 Numbers whose third-largest divisor is prime.

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

Author

Gus Wiseman, Oct 16 2019

Keywords

• nonn

Examples

			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}
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

A subset of A002808 and superset of A006881.

Numbers whose third-smallest divisor is prime are A119313.

Third-smallest divisor is A292269.

Cf. A000005, A020639, A027750, A033676, A060775, A067513, A088725.

Programs

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]]]&]

PARI

isA328338(n) = { my(u=numdiv(n)); ((u>2)&&isprime(divisors(n)[u-2])); }; \\ Antti Karttunen, Oct 17 2019