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A274435 Numbers having equal numbers of distinct prime factors of forms 3*k+1 and 3*k+2. 3
1, 3, 9, 14, 26, 27, 28, 35, 38, 42, 52, 56, 62, 65, 74, 76, 77, 78, 81, 84, 86, 95, 98, 104, 105, 112, 114, 119, 122, 124, 126, 134, 143, 146, 148, 152, 155, 156, 158, 161, 168, 172, 175, 185, 186, 194, 195, 196, 203, 206, 208, 209, 215, 218, 221, 222, 224 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence and A274436 and A274437 partition the positive integers.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000

EXAMPLE

76 = 2^2 19^1, so that the number of distinct primes 3*k+1 is 1 and the number of distinct primes 3*k + 2 is 1.

3 and 9 also qualify, since they have no prime factors of either type.

MATHEMATICA

g[n_] := Map[First, FactorInteger[n]] ; z = 5000;

p1 = Select[Prime[Range[z]], Mod[#, 3] == 1 &];

p2 = Select[Prime[Range[z]], Mod[#, 3] == 2 &];

q1[n_] := Length[Intersection[g[n], p1]]

q2[n_] := Length[Intersection[g[n], p2]]

Select[Range[z], q1[#] == q2[#] &]; (* A274435 *)

Select[Range[z], q1[#] < q2[#] &]; (* A274436 *)

Select[Range[z], q1[#] > q2[#] &]; (* A274437 *)

PROG

(PARI) is(n) = my(f=factor(n)[, 1]~, i=0, j=0); for(k=1, #f, if(!((f[k]-1)%3), i++); if(!((f[k]-2)%3), j++)); i==j \\ Felix Fröhlich, Jul 09 2018

CROSSREFS

Cf. A274436, A274437.

Sequence in context: A309149 A294480 A195972 * A136562 A305342 A197274

Adjacent sequences:  A274432 A274433 A274434 * A274436 A274437 A274438

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jul 19 2016

STATUS

approved

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Last modified July 24 23:25 EDT 2021. Contains 346273 sequences. (Running on oeis4.)