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A033831 Number of numbers d dividing n such that d >= 3 and 1 <= n/d <= d-2. 11
0, 0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 4, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 2, 4, 1, 2, 2, 4, 1, 3, 1, 3, 3, 2, 1, 5, 1, 3, 2, 3, 1, 4, 2, 3, 2, 2, 1, 6, 1, 2, 3, 3, 2, 4, 1, 3, 2, 4, 1, 5, 1, 2, 3, 3, 2, 4, 1, 5, 2, 2, 1, 6, 2, 2, 2, 4, 1, 5, 2, 3, 2, 2, 2, 6, 1, 3, 3, 4, 1, 4, 1, 4, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

FORMULA

G.f.: Sum_{n>=1} x^(n^2+2*n)/(1-x^n). - Vladeta Jovovic, May 13 2008

MAPLE

with(numtheory): for n from 1 to 200 do it := divisors(n): count := 0: for i from 1 to nops(it) do if it[i]>=3 and 1<=n/it[i] and n/it[i]<=(it[i]-2) then count := count+1 fi :od: printf(`%d, `, count) od:

MATHEMATICA

a[n_] := DivisorSum[n, 1&, # > 2 && n/# < #-1 &]; Array[a, 100] (* Amiram Eldar, Jun 11 2019 *)

PROG

(PARI) a(n) = sumdiv(n, d, (d>=3) && (q=n/d) && (q>=1) && (q<=d-2)); \\ Michel Marcus, Nov 05 2014

CROSSREFS

Sequence in context: A087976 A227903 A117277 * A033105 A106703 A127267

Adjacent sequences:  A033828 A033829 A033830 * A033832 A033833 A033834

KEYWORD

easy,nonn

AUTHOR

Naohiro Nomoto

EXTENSIONS

More terms from James A. Sellers, Jun 20 2000

STATUS

approved

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Last modified February 28 10:22 EST 2020. Contains 332323 sequences. (Running on oeis4.)