A348955 - OEIS

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A348955

a(1) = 1; a(n) = Sum_{d|n, d <= sqrt(n)} a(d)^2.

1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 6, 1, 3, 1, 6, 2, 2, 1, 7, 2, 2, 2, 6, 1, 4, 1, 6, 2, 2, 2, 11, 1, 2, 2, 7, 1, 7, 1, 6, 3, 2, 1, 11, 2, 3, 2, 6, 1, 7, 2, 7, 2, 2, 1, 12, 1, 2, 3, 10, 2, 7, 1, 6, 2, 4, 1, 15, 1, 2, 3, 6, 2, 7, 1, 11, 6, 2, 1, 12, 2, 2, 2, 10, 1, 12

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

FORMULA

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

a(4^n) = A067868(n).

MATHEMATICA

a[1] = 1; a[n_] := a[n] = DivisorSum[n, a[#]^2 &, # <= Sqrt[n] &]; Table[a[n], {n, 90}]

PROG

(PARI) A348955(n) = if(1==n, n, sumdiv(n, d, if((d*d)<=n, A348955(d)^2, 0))); \\ Antti Karttunen, Nov 05 2021