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A175705
Convolution square of A001157 (the sum of squared divisors).
1
1, 10, 45, 142, 362, 780, 1561, 2762, 4808, 7570, 12034, 17482, 26072, 35884, 50909, 67012, 92111, 116950, 155720, 193564, 250914, 304244, 389286, 461654, 578952, 680944, 839304, 970094, 1188924, 1354164, 1637145, 1858344, 2215866, 2485068
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{k=1..n} A001157(k)* A001157(n+1-k).
G.f.: (1/x)*(Sum_{k>=1} k^2*x^k/(1 - x^k))^2. - Ilya Gutkovskiy, Jan 01 2017
MAPLE
with(numtheory): T:=array(1..200):for p from 1 to 200 do: liste:=divisors(p) :s2:=sum(liste[i]^2, i=1..nops(liste)):T[p] :=s2 :od : for n from 1 to 100 do: printf(`%d, `, sum (T[k]*T[n+1-k], k=1..n)):od:
MATHEMATICA
a[n_] := Sum[DivisorSigma[2, k] * DivisorSigma[2, n + 1 - k], {k, 1, n}]; Array[a, 34] (* Amiram Eldar, Jul 31 2019 *)
CROSSREFS
Cf. A001157.
Sequence in context: A037270 A027800 A005714 * A143671 A221532 A241432
KEYWORD
nonn
AUTHOR
Michel Lagneau, Aug 10 2010
EXTENSIONS
Definition slightly rephrased by R. J. Mathar, Aug 19 2010
STATUS
approved