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A376270 a(n) is the product of the leading digit of n and the sum of the squares of its digits.

%I A376270 #24 Sep 28 2024 19:42:15
%S A376270 0,1,8,27,64,125,216,343,512,729,1,2,5,10,17,26,37,50,65,82,8,10,16,
%T A376270 26,40,58,80,106,136,170,27,30,39,54,75,102,135,174,219,270,64,68,80,
%U A376270 100,128,164,208,260,320,388,125,130,145,170,205,250,305,370,445,530,216,222,240,270,312,366
%N A376270 a(n) is the product of the leading digit of n and the sum of the squares of its digits.
%H A376270 Alois P. Heinz, <a href="/A376270/b376270.txt">Table of n, a(n) for n = 0..10000</a>
%H A376270 N. Bradley Fox et al., <a href="https://arxiv.org/abs/2409.09863">Elated Numbers</a>, arXiv:2409.09863 [math.NT], 2024.
%F A376270 a(n) = A000030(n)*A003132(n).
%p A376270 a:= n-> (l-> l[-1]*add(i^2, i=l))(convert(n, base, 10)):
%p A376270 seq(a(n), n=0..65);  # _Alois P. Heinz_, Sep 18 2024
%t A376270 a[n_]:=First[d=IntegerDigits[n]]Norm[d]^2; Array[a,66,0] (* _Stefano Spezia_, Sep 18 2024 *)
%o A376270 (PARI) a(n) = if (n, my(d=digits(n)); d[1]*norml2(d), 0);
%o A376270 (Python)
%o A376270 def a(n): return (d:=list(map(int, str(n))))[0] * sum(di*di for di in d)
%o A376270 print([a(n) for n in range(66)]) # _Michael S. Branicky_, Sep 18 2024
%Y A376270 Cf. A000030, A003132.
%Y A376270 b-elated function: A000120 (2), A376270 (10).
%K A376270 nonn,look,base
%O A376270 0,3
%A A376270 _Michel Marcus_, Sep 18 2024