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A067340 Numbers k such that (number of distinct prime factors of k) divides (number of prime factors of k). 12
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 46, 47, 49, 51, 53, 54, 55, 56, 57, 58, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 81, 82, 83, 85, 86, 87, 88, 89, 91 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..20000

FORMULA

A001222(k)/A001221(k) is an integer.

EXAMPLE

Primes and prime powers are included in this sequence. Another example: 24, since A001222(24)/A001222(24) = 4/2 = 2.

MATHEMATICA

ff[x_] := Flatten[FactorInteger[x]]; f1[x_] := Length[FactorInteger[x]]; f2[x_] := Apply[Plus, Table[Part[ff[x], 2*w], {w, 1, f1[x]}]]; Do[s=f2[n]/f1[n]; If[IntegerQ[s], Print[n]], {n, 2, 256}]

Select[Range[2, 91], Divisible[PrimeOmega[#], PrimeNu[#]]&] (* Ivan N. Ianakiev, Dec 07 2015 *)

PROG

(PARI) v=[]; for(n=2, 100, if(denominator(bigomega(n)/omega(n)) == 1, v=concat(v, n))); v

(PARI) is(n)=my(f=factor(n)[, 2]); #f && vecsum(f)%#f==0 \\ Charles R Greathouse IV, Oct 15 2015

CROSSREFS

Cf. A001221, A001222, A245080.

Sequence in context: A107909 A255724 A285100 * A263837 A283550 A271113

Adjacent sequences:  A067337 A067338 A067339 * A067341 A067342 A067343

KEYWORD

nonn

AUTHOR

Labos Elemer, Jan 16 2002

STATUS

approved

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Last modified January 22 23:00 EST 2019. Contains 319365 sequences. (Running on oeis4.)