

A318400


Numbers whose prime indices are all powers of 2 (including 1).


10



1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 19, 21, 24, 27, 28, 32, 36, 38, 42, 48, 49, 53, 54, 56, 57, 63, 64, 72, 76, 81, 84, 96, 98, 106, 108, 112, 114, 126, 128, 131, 133, 144, 147, 152, 159, 162, 168, 171, 189, 192, 196, 212, 216, 224, 228, 243, 252, 256, 262
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OFFSET

1,2


COMMENTS

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.


LINKS

Table of n, a(n) for n=1..61.


EXAMPLE

The sequence of all integer partitions whose parts are all powers of 2 (including 1) begins: (), (1), (2), (11), (21), (4), (111), (22), (211), (41), (1111), (221), (8), (42), (2111), (222), (411), (11111), (2211), (81), (421), (21111), (44).


MATHEMATICA

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
pow2Q[n_]:=Or[n==1, MatchQ[FactorInteger[n], {{2, _}}]];
Select[Range[100], And@@pow2Q/@primeMS[#]&]


CROSSREFS

Cf. A003963, A018819, A033844, A056239, A106349, A112798, A302242, A302491, A322551.
Sequence in context: A010408 A010455 A269804 * A219174 A108319 A177500
Adjacent sequences: A318397 A318398 A318399 * A318401 A318402 A318403


KEYWORD

nonn


AUTHOR

Gus Wiseman, Dec 16 2018


STATUS

approved



