A324927 Matula-Goebel numbers of rooted trees of depth 2. Numbers that are not powers of 2 but whose prime indices are all powers of 2.

3, 6, 7, 9, 12, 14, 18, 19, 21, 24, 27, 28, 36, 38, 42, 48, 49, 53, 54, 56, 57, 63, 72, 76, 81, 84, 96, 98, 106, 108, 112, 114, 126, 131, 133, 144, 147, 152, 159, 162, 168, 171, 189, 192, 196, 212, 216, 224, 228, 243, 252, 262, 266, 288, 294, 304, 311, 318

Offset

1,1

Comments

Numbers n such that A109082(n) = 2.

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Also Heinz numbers of integer partitions into powers of 2 with at least one part > 1 (counted by A102378).

Links

Table of n, a(n) for n=1..58.

Example

The sequence of terms together with their prime indices begins:
   3: {2}
   6: {1,2}
   7: {4}
   9: {2,2}
  12: {1,1,2}
  14: {1,4}
  18: {1,2,2}
  19: {8}
  21: {2,4}
  24: {1,1,1,2}
  27: {2,2,2}
  28: {1,1,4}
  36: {1,1,2,2}
  38: {1,8}
  42: {1,2,4}
  48: {1,1,1,1,2}
  49: {4,4}
  53: {16}
  54: {1,2,2,2}
  56: {1,1,1,4}

Mathematica

Select[Range[100], And[!IntegerQ[Log[2, #]], And@@Cases[FactorInteger[#], {p_, _}:>IntegerQ[Log[2, PrimePi[p]]]]]&]

Crossrefs

Cf. A000081, A000720, A003963, A007097, A018819, A033844, A056239, A102378, A112798, A302242, A318400, A324928, A324929.

Sequence in context: A176409 A284473 A120684 * A026227 A026232 A286802

Adjacent sequences: A324924 A324925 A324926 * A324928 A324929 A324930

Keyword

nonn

Author

Gus Wiseman, Mar 21 2019

Status

approved