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A023534 Numbers n such that the largest power of 2 dividing n equals 2^omega(n). 2
1, 2, 12, 20, 28, 36, 44, 52, 68, 76, 92, 100, 108, 116, 120, 124, 148, 164, 168, 172, 188, 196, 212, 236, 244, 264, 268, 280, 284, 292, 312, 316, 324, 332, 356, 360, 388, 404, 408, 412, 428, 436, 440, 452, 456, 484, 500, 504, 508, 520, 524, 548, 552, 556 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

That is, numbers such that A001221(n) is equal to A007814(n).

omega(n) = A001221(n) is the number of distinct primes dividing n.

And A007814(n) is the exponent of the highest power of 2 dividing n.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

EXAMPLE

omega(12)=2 and 4=2^2 is the largest power of 2 dividing 12, hence 12 is in the sequence.

MATHEMATICA

Select[Range[600], IntegerExponent[#, 2]==PrimeNu[#]&] (* Harvey P. Dale, Jun 26 2011 *)

PROG

(PARI) isok(n) = omega(n) == valuation(n, 2); \\ Michel Marcus, Apr 16 2015

CROSSREFS

Cf. A039700, A001221 (omega), A007814 (2-adic valuation).

Sequence in context: A137311 A032407 A136725 * A286683 A326238 A226399

Adjacent sequences:  A023531 A023532 A023533 * A023535 A023536 A023537

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Sep 04 2002

STATUS

approved

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Last modified April 3 20:29 EDT 2020. Contains 333199 sequences. (Running on oeis4.)