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

1,1

Links

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

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.

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

Sequence in context: A331231 A130763 A332269 * A365535 A120497 A036436

Adjacent sequences: A328335 A328336 A328337 * A328339 A328340 A328341

Keyword

nonn

Author

Gus Wiseman, Oct 16 2019

Status

approved