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

0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1, 2, 5, 10, 17, 26, 37, 50, 65, 82, 8, 10, 16, 26, 40, 58, 80, 106, 136, 170, 27, 30, 39, 54, 75, 102, 135, 174, 219, 270, 64, 68, 80, 100, 128, 164, 208, 260, 320, 388, 125, 130, 145, 170, 205, 250, 305, 370, 445, 530, 216, 222, 240, 270, 312, 366

Offset: 0

Author

Michel Marcus, Sep 18 2024

Keywords

• nonn
• look
• base

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000
• N. Bradley Fox et al., Elated Numbers, arXiv:2409.09863 [math.NT], 2024.

Crossrefs

Cf. A000030, A003132.

b-elated function: A000120 (2), A376270 (10).

Programs

Maple

a:= n-> (l-> l[-1]*add(i^2, i=l))(convert(n, base, 10)):
seq(a(n), n=0..65);  # Alois P. Heinz, Sep 18 2024

Mathematica

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

PARI

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

Python

def a(n): return (d:=list(map(int, str(n))))[0] * sum(di*di for di in d)
print([a(n) for n in range(66)]) # Michael S. Branicky, Sep 18 2024

Formula

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