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A304250 Perfect powers whose prime factors span an initial interval of prime numbers. 3
4, 8, 16, 32, 36, 64, 128, 144, 216, 256, 324, 512, 576, 900, 1024, 1296, 1728, 2048, 2304, 2916, 3600, 4096, 5184, 5832, 7776, 8100, 8192, 9216, 11664, 13824, 14400, 16384, 20736, 22500, 26244, 27000, 32400, 32768, 36864, 44100, 46656, 57600, 65536, 72900 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The multiset of prime indices of a(n) is the a(n)-th row of A112798. This multiset is normal, meaning it spans an initial interval of positive integers, and periodic, meaning its multiplicities have a common divisor greater than 1.

LINKS

Table of n, a(n) for n=1..44.

FORMULA

Intersection of A001597 and A055932.

EXAMPLE

Sequence of all normal periodic multisets begins

4:    {1,1}

8:    {1,1,1}

16:   {1,1,1,1}

32:   {1,1,1,1,1}

36:   {1,1,2,2}

64:   {1,1,1,1,1,1}

128:  {1,1,1,1,1,1,1}

144:  {1,1,1,1,2,2}

216:  {1,1,1,2,2,2}

256:  {1,1,1,1,1,1,1,1}

324:  {1,1,2,2,2,2}

512:  {1,1,1,1,1,1,1,1,1}

576:  {1,1,1,1,1,1,2,2}

900:  {1,1,2,2,3,3}

1024: {1,1,1,1,1,1,1,1,1,1}

MATHEMATICA

Select[Range[1000], FactorInteger[#][[-1, 1]]==Prime[Length[FactorInteger[#]]]&&GCD@@FactorInteger[#][[All, 2]]>1&]

CROSSREFS

Cf. A000837, A000961 A001597, A007916, A018783, A052409, A052410, A055932, A056239, A112798, A178472, A303431, A303709, A304450.

Sequence in context: A181800 A319180 A075090 * A322793 A283052 A088259

Adjacent sequences:  A304247 A304248 A304249 * A304251 A304252 A304253

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 13 2018

STATUS

approved

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Last modified November 17 11:02 EST 2019. Contains 329226 sequences. (Running on oeis4.)