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A300410 Number of centered square numbers dividing n. 3
1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 2, 1, 2, 1, 2, 1, 1, 3, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

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

Eric Weisstein's World of Mathematics, Centered Square Number

Index entries for sequences related to centered polygonal numbers

FORMULA

G.f.: Sum_{k>=0} x^(2*k*(k+1)+1)/(1 - x^(2*k*(k+1)+1)).

EXAMPLE

a(26) = 2 because 26 has 4 divisors {1, 2, 13, 26} among which 2 divisors {1, 13} are centered square numbers.

MAPLE

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

V:= Vector(N, 1):

for k from 1 do

  m:= 2*k*(k+1)+1;

  if m > N then break fi;

  r:= [seq(i, i=m..N, m)];

  V[r]:= map(t->t+1, V[r]);

od:

convert(V, list); # Robert Israel, Mar 05 2018

MATHEMATICA

nmax = 100; Rest[CoefficientList[Series[Sum[x^(2 k (k + 1) + 1)/(1 - x^(2 k (k + 1) + 1)), {k, 0, nmax}], {x, 0, nmax}], x]]

CROSSREFS

Cf. A001844, A046951, A279496, A300409.

Sequence in context: A318498 A093997 A157196 * A293451 A063014 A286361

Adjacent sequences:  A300407 A300408 A300409 * A300411 A300412 A300413

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 05 2018

STATUS

approved

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Last modified September 19 07:08 EDT 2021. Contains 347554 sequences. (Running on oeis4.)