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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. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 19 09:24 EDT 2019. Contains 323390 sequences. (Running on oeis4.)