A067868 -id:A067868 - cp's OEIS frontend

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

Offset: 1

Ilya Gutkovskiy, Nov 04 2021

nonn

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

Cf. A008578 (positions of 1's), A067868, A068108, A082588, A337135, A348956.

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

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

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

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

A058039 a(n) = a(n-1) + 2*a(floor(n/2)) if n > 0, otherwise 1.

Original entry on oeis.org

1, 3, 9, 15, 33, 51, 81, 111, 177, 243, 345, 447, 609, 771, 993, 1215, 1569, 1923, 2409, 2895, 3585, 4275, 5169, 6063, 7281, 8499, 10041, 11583, 13569, 15555, 17985, 20415, 23553, 26691, 30537, 34383, 39201, 44019, 49809, 55599, 62769, 69939, 78489, 87039

Offset: 0

Reinhard Zumkeller, Feb 16 2002

nonn

G. C. Greubel, Table of n, a(n) for n = 0..1000

Cf. A000123, A002061, A067868, A347027.

[1] cat [n le 2 select 3^n else Self(n-1) + 2*Self(Floor(n/2)): n in [1..51]]; // G. C. Greubel, Feb 10 2021

a[n_]:= a[n] = If[n==0, 1, a[n-1] + 2*a[Floor[n/2]]];
Table[a[n], {n, 0, 50}] (* G. C. Greubel, Feb 10 2021 *)

a(n) = if (n==0, 1, a(n-1)+2*a(n\2)); \\ Michel Marcus, Feb 04 2021

def a(n): return 1 if n == 0 else a(n-1) + 2*a(n//2)
print([a(n) for n in range(44)]) # Michael S. Branicky, Feb 04 2021

a(n) = 1 + 2 * Sum_{k=1..n} a(floor(k/2)). - Ilya Gutkovskiy, Aug 15 2021

Name corrected by and more terms from Michael S. Branicky, Feb 04 2021

cp's OEIS Frontend

A348955 a(1) = 1; a(n) = Sum_{d|n, d <= sqrt(n)} a(d)^2.

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