A275547 Numbers n that have an equal number of even and odd values of A001221(k) for 1 <= k <= n.
2, 40, 46, 48, 50, 7960, 7962, 7984, 7986, 8808, 8810, 8812, 8816, 8822, 8824, 8826, 8828, 8830, 8836, 8844, 8846, 8848, 8850, 8854, 8856, 8858, 8860, 8862, 8864, 8866, 8872, 8878, 8970, 8972, 8974, 9064, 9078, 9080, 9082, 9084, 9086, 9088, 9096, 9164, 9220
Offset: 1
Keywords
Examples
a(2) = 40 because if we check omega(n) = A001221(n) for each n = 1..40, then half will be even numbers and half will be odd numbers.
Links
- Giovanni Resta, Table of n, a(n) for n = 1..10000
Programs
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Maple
omega:= n-> nops(numtheory[factorset](n)): b:= proc(n) option remember; (-1)^omega(n)+`if`(n>1, b(n-1), 0) end: a:= proc(n) option remember; local k; for k from 1+ `if`(n=1, 0, a(n-1)) while b(k)<>0 do od; k end: seq(a(n), n=1..50); # Alois P. Heinz, Aug 02 2016 -
Mathematica
a[1] = 2; a[n_] := a[n] = Block[{k = a[n-1], s=0}, While[(s += (-1)^ PrimeNu[++k]) != 0]; k]; Array[a, 100] (* Giovanni Resta, Aug 03 2016 *) -
PARI
is(n) = my(i=0, j=0); for(k=1, n, if(omega(k)%2==0, i++, j++)); if(i==j, return(1), return(0)) \\ Felix Fröhlich, Aug 02 2016
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PARI
isok(n) = {my(v = vector(n, k, omega(k))); #select(x->x % 2 == 1, v) == n/2;} \\ Michel Marcus, Aug 02 2016
Formula
A174863(a(n)) = 0. - Alois P. Heinz, Aug 02 2016
Extensions
More terms from Alois P. Heinz, Aug 02 2016
Comments