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A323056 Numbers with exactly five distinct exponents in their prime factorization, or five distinct parts in their prime signature. 5
174636000, 206388000, 244490400, 261954000, 269892000, 274428000, 288943200, 291060000, 301644000, 309582000, 343980000, 349272000, 365148000, 366735600, 377848800, 383292000, 404838000, 411642000, 412776000, 422301600, 433414800, 449820000, 452466000, 457380000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The first term is A006939(5) = 174636000.

Positions of 5's in A071625.

Numbers k such that A001221(A181819(k)) = 5.

LINKS

David A. Corneth, Table of n, a(n) for n = 1..10000

EXAMPLE

174636000 = 2^5 * 3^4 * 5^3 * 7^2 * 11^1 has five distinct exponents so belongs to the sequence.

MATHEMATICA

Select[Range[300000000], Length[Union[Last/@FactorInteger[#]]]==5&]

PROG

(PARI) is(n) = #Set(factor(n)[, 2]) == 5 \\ David A. Corneth, Jan 12 2019

CROSSREFS

One distinct exponent: A062770 or A072774.

Two distinct exponents: A323055.

Three distinct exponents: A323024.

Four distinct exponents: A323025.

Five distinct exponents: A323056.

Cf. A001221, A001222, A006939, A051270, A059404, A071625, A118914, A181819, A182855, A323014, A323022, A323024.

Sequence in context: A003843 A093047 A093046 * A300555 A306876 A213966

Adjacent sequences:  A323053 A323054 A323055 * A323057 A323058 A323059

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 03 2019

EXTENSIONS

a(13)-a(24) from Daniel Suteu, Jan 12 2019

STATUS

approved

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Last modified September 17 14:07 EDT 2021. Contains 347478 sequences. (Running on oeis4.)