A367544 Euclid's triangle A217831 represented as decimal numbers.

0, 3, 2, 6, 10, 30, 34, 126, 170, 438, 650, 2046, 2210, 8190, 10794, 27030, 43690, 131070, 141474, 524286, 666250, 1781046, 2794154, 8388606, 9054370, 32472030, 44731050, 115043766, 176859690, 536870910, 545925250, 2147483646, 2863311530, 7358604726, 11453115050

Offset

0,2

Comments

The decimal equivalents of A367547.

Links

Table of n, a(n) for n=0..34.

Formula

a(n) = Sum_{k=0..n} 2^k * |(n - k | k)|, where (a | b) denotes the Kronecker symbol.

a(n) = Sum_{k=0..n} [gcd(k, n) = 1] * 2^k, where [] is the Iverson bracket.

Maple

KS := (n, k) -> NumberTheory:-KroneckerSymbol(n, k):
A367544 := n -> local k; add(2^k * abs(KS(n - k, k)), k = 0..n):
seq(A367544(n), n = 0..34);

Mathematica

A367544[n_]:=FromDigits[Boole[CoprimeQ[n, Range[0, n]]], 2];
Array[A367544, 50, 0] (* Paolo Xausa, Nov 24 2023 *)

Prog

(SageMath)  # For Python include 'import math' for math.gcd.
def a(n):
    cop = [int(gcd(i, n) == 1) for i in range(n + 1)]
    return sum(p * 2^k for k, p in enumerate(cop))
print([a(n) for n in range(35)])
(PARI) a(n) = sum(k=0, n, 2^k*abs(kronecker(n-k, k))); \\ Michel Marcus, Nov 23 2023
(PARI) a(n) = fromdigits(vector(n+1, i, gcd(i-1, n)==1), 2); \\ Michel Marcus, Nov 24 2023
(Python)
from math import gcd
def A367544(n): return sum(1<<k for k in range(n+1) if gcd(n, k)==1) # Chai Wah Wu, Nov 24 2023

Crossrefs

Cf. A217831, A000010, A023896, A055034, A349136, A367545, A367546, A367547.

Sequence in context: A210748 A331889 A369247 * A340612 A362373 A364929

Adjacent sequences: A367541 A367542 A367543 * A367545 A367546 A367547

Keyword

nonn,base

Author

Peter Luschny, Nov 22 2023

Status

approved