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A224834
a(n) = Sum {d|n, d <= n^(1/2)} tau(d)^2.
2
1, 1, 1, 5, 1, 5, 1, 5, 5, 5, 1, 9, 1, 5, 5, 14, 1, 9, 1, 14, 5, 5, 1, 18, 5, 5, 5, 14, 1, 13, 1, 14, 5, 5, 5, 34, 1, 5, 5, 18, 1, 25, 1, 14, 9, 5, 1, 34, 5, 9, 5, 14, 1, 25, 5, 18, 5, 5, 1, 38, 1, 5, 9, 30, 5, 25, 1, 14, 5, 13, 1, 50, 1, 5, 9
OFFSET
1,4
LINKS
FORMULA
If p is prime, a(p^k) = A000330(1+floor(k/2)). - Robert Israel, Nov 30 2016
MAPLE
f:= proc(n) add(numtheory:-tau(d)^2, d = select(t -> (t^2<=n), numtheory:-divisors(n))) end proc:
map(f, [$1..100]); # Robert Israel, Nov 30 2016
MATHEMATICA
a[n_] := DivisorSum[n, DivisorSigma[0, #]^2 &, #^2 <= n &]; Array[a, 100] (* Amiram Eldar, Aug 29 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, (d<=sqrtn(n, 2))*numdiv(d)^2) \\ Michel Marcus, Jul 21 2013
(PARI) a(n)=my(s=sqrtint(n)); sumdiv(n, d, if(d<=s, numdiv(d)^2)) \\ Charles R Greathouse IV, Jul 22 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Jul 21 2013
STATUS
approved