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A193022 Numbers n such that n divides (omega(n)*bigomega(n))^n. 1
1, 4, 12, 16, 18, 27, 64, 80, 96, 144, 200, 216, 256, 324, 448, 486, 500, 729, 768, 1024, 1152, 1250, 1568, 1728, 2560, 2592, 3125, 3840, 3888, 4096, 5488, 5760, 5832, 6144, 6400, 8640, 8748, 9216, 9600, 11264, 12960, 13122, 13824, 14400, 16000, 16384 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Here omega(n) = A001221(n) is number of distinct primes dividing n and bigomega(n) = A001222(n) is number of prime divisors of n counted with multiplicity. This is not a subsequence of A067575: 3840 belongs to this sequence but not to A067575.

Also numbers n such that rad(n) = rad(omega(n)*bigomega(n)) where rad is A007947. [Charles R Greathouse IV, Jul 18 2011]

LINKS

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..400

MATHEMATICA

Select[Range[12960], PowerMod[PrimeNu[#] PrimeOmega[#], #, #] == 0 &] (* T. D. Noe, Jul 14 2011 *)

PROG

(PARI) for(n=1, 2^14, if(lift(Mod((omega(n)*bigomega(n))^n, n))==0, print1(n, ", "))); \\ Arkadiusz Wesolowski, Jul 18 2011

CROSSREFS

Cf. A067575, A001221, A001222, A007947.

Sequence in context: A328840 A255411 A067575 * A145199 A082420 A259118

Adjacent sequences:  A193019 A193020 A193021 * A193023 A193024 A193025

KEYWORD

nonn

AUTHOR

Arkadiusz Wesolowski, Jul 14 2011

STATUS

approved

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Last modified March 30 08:45 EDT 2020. Contains 333123 sequences. (Running on oeis4.)