cp's OEIS Frontend

A363735 a(n) = Sum_{k=0..n} n^notdivides(k, n), where notdivides(k, n) = 0 if k divides n, otherwise 1.

%I A363735 #22 Aug 06 2023 17:51:08
%S A363735 1,2,4,8,11,22,22,44,44,66,74,112,90,158,158,184,197,274,240,344,306,
%T A363735 382,422,508,416,578,602,652,650,814,698,932,870,994,1058,1124,1017,
%U A363735 1334,1334,1408,1328,1642,1478,1808,1722,1806,1982,2164,1882,2306,2256,2452
%N A363735 a(n) = Sum_{k=0..n} n^notdivides(k, n), where notdivides(k, n) = 0 if k divides n, otherwise 1.
%H A363735 Peter Luschny, <a href="/A363735/b363735.txt">Table of n, a(n) for n = 0..10000</a>
%F A363735 a(n) = (1 - n) * tau(n) + n * (1 + n) for n >= 1, where tau = A000005.
%F A363735 a(n) + A363734(n) = (n + 1)^2.
%F A363735 a(n) - A363734(n) = A363421(n).
%t A363735 A363735[n_]:=If[n==0,1,n(n+1)+(1-n)DivisorSigma[0,n]];Array[A363735,100,0] (* _Paolo Xausa_, Aug 06 2023 *)
%o A363735 (SageMath)
%o A363735 print([sum(n^(not k.divides(n)) for k in srange(n + 1)) for n in srange(52)])
%o A363735 (Python)
%o A363735 from sympy import divisor_count
%o A363735 def A363735(n): return n*(n+1)-(n-1)*divisor_count(n) if n else 1 # _Chai Wah Wu_, Jun 28 2023
%Y A363735 Cf. A113704, A000005, A363734, A363421.
%K A363735 nonn
%O A363735 0,2
%A A363735 _Peter Luschny_, Jun 27 2023