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A333806 Number of distinct prime divisors of n that are < sqrt(n). 35
0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 3, 0, 1, 1, 1, 1, 2, 0, 1, 1, 2, 0, 2, 0, 1, 2, 1, 0, 2, 0, 2, 1, 1, 0, 2, 1, 2, 1, 1, 0, 3, 0, 1, 2, 1, 1, 2, 0, 1, 1, 3, 0, 2, 0, 1, 2, 1, 1, 2, 0, 2, 1, 1, 0, 3, 1, 1, 1, 1, 0, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,12

COMMENTS

a(n) = 0 if and only if n = p^k where p is prime and k is 0, 1, or 2. - Charles R Greathouse IV, Apr 07 2020

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

G.f.: Sum_{k>=1} x^(prime(k)*(prime(k) + 1)) / (1 - x^prime(k)).

MAPLE

N:= 100: # for a(1)..a(N)

V:= Vector(N):

p:= 1:

do

  p:= nextprime(p);

  if p^2 >= N then break fi;

  L:= [seq(p*k, k=p+1..N/p)];

  V[L]:= V[L]+~1

od:

convert(V, list); # Robert Israel, Apr 07 2020

MATHEMATICA

Table[DivisorSum[n, 1 &, # < Sqrt[n] && PrimeQ[#] &], {n, 1, 90}]

nmax = 90; CoefficientList[Series[Sum[x^(Prime[k] (Prime[k] + 1))/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

PROG

(PARI) a(n)=my(f=factor(n)[, 1]); sum(i=1, #f, f[i]^2<n) \\ Charles R Greathouse IV, Apr 07 2020

CROSSREFS

Cf. A001221, A056924, A063962, A333805, A333808.

Sequence in context: A117454 A115357 A171182 * A340832 A063962 A084114

Adjacent sequences:  A333803 A333804 A333805 * A333807 A333808 A333809

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 05 2020

STATUS

approved

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Last modified May 14 13:50 EDT 2021. Contains 343884 sequences. (Running on oeis4.)