A376270 - OEIS

%I #27 Sep 26 2025 09:16:42

%S 0,1,8,27,64,125,216,343,512,729,1,2,5,10,17,26,37,50,65,82,8,10,16,

%T 26,40,58,80,106,136,170,27,30,39,54,75,102,135,174,219,270,64,68,80,

%U 100,128,164,208,260,320,388,125,130,145,170,205,250,305,370,445,530,216,222,240,270,312,366

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

%H Alois P. Heinz, <a href="/A376270/b376270.txt">Table of n, a(n) for n = 0..10000</a>

%H N. Bradley Fox et al., <a href="https://arxiv.org/abs/2409.09863">Elated Numbers</a>, arXiv:2409.09863 [math.NT], 2024.

%F a(n) = A000030(n)*A003132(n).

%p a:= n-> (l-> l[-1]*add(i^2, i=l))(convert(n, base, 10)):

%p seq(a(n), n=0..65);  # _Alois P. Heinz_, Sep 18 2024

%t a[n_]:=First[d=IntegerDigits[n]]Norm[d]^2; Array[a,66,0] (* _Stefano Spezia_, Sep 18 2024 *)

%o (PARI) a(n) = if (n, my(d=digits(n)); d[1]*norml2(d), 0);

%o (Python)

%o def a(n): return (d:=list(map(int, str(n))))[0] * sum(di*di for di in d)

%o print([a(n) for n in range(66)]) # _Michael S. Branicky_, Sep 18 2024

%Y Cf. A000030, A003132.

%Y b-elated function: A000120 (2), this sequence (10).

%K nonn,look,base

%O 0,3

%A _Michel Marcus_, Sep 18 2024