This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A368980 #12 Nov 19 2024 13:19:07
%S A368980 1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,
%T A368980 0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,
%U A368980 0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0
%N A368980 The number of exponential divisors of n that are squares (A000290).
%H A368980 Amiram Eldar, <a href="/A368980/b368980.txt">Table of n, a(n) for n = 1..10000</a>
%F A368980 a(n^2) = A049419(n). [corrected by _Ridouane Oudra_, Nov 19 2024]
%F A368980 Multiplicative with a(p^e) = A183063(e), or equivalently, a(p^e) = 0 if e is odd, and A000005(e/2) if e is even.
%F A368980 a(n) >= 0, with equality if and only if n is not a square number (A000037).
%F A368980 a(n) <= A049419(n), with equality if and only if n = 1.
%F A368980 Sum_{k=1..n} a(k) ~ c * sqrt(n), where c = 1.602317... (A327837).
%t A368980 f[p_, e_] := If[OddQ[e], 0, DivisorSigma[0, e/2]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A368980 (PARI) a(n) = vecprod(apply(x -> if(x%2, 0, numdiv(x/2)), factor(n)[, 2]));
%Y A368980 Cf. A000005, A000037, A000290, A049419, A183063, A322791, A327837, A368979.
%Y A368980 Similar sequences: A046951, A056624, A358260, A368978.
%K A368980 nonn,easy,mult
%O A368980 1,16
%A A368980 _Amiram Eldar_, Jan 11 2024