OFFSET
1,1
COMMENTS
From Peter Luschny, Jul 19 2023: (Start)
If the name means 'Numbers k such that (number of prime factors of k) is divisible by the (number of distinct prime factors of k)', then 1 has to be prepended to the data since A001221(1) = A001222(1) = 0 and 0 is divisible by 0.
Note that the expression 'A001222(k)/A001221(k)' is read as 'the quotient of A001222(k) and A001221(k)' and is not defined in the case k = 1 because A001221(1) = 0. On the other hand, the expression 'A001221(k) | A001222(k)' is read as 'A001221(k) divides A001222(k)' and is well defined also if k = 1 and has the value 'True'. (End)
LINKS
Stanislav Sykora, Table of n, a(n) for n = 1..20000
EXAMPLE
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
(SageMath)
def dpf(n): return sloane.A001221(n)
def tpf(n): return sloane.A001222(n)
a = [k for k in range(1, 92) if ZZ(dpf(k)).divides(tpf(k))]
print(a) # Peter Luschny, Jul 19 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Jan 16 2002
STATUS
approved