cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A064946 a(n) = Sum_{i|n, j|n, j>i} j.

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%I A064946 #24 Aug 14 2025 03:58:37
%S A064946 0,2,3,10,5,26,7,34,21,42,11,104,13,58,58,98,17,152,19,165,80,90,23,
%T A064946 324,55,106,102,227,29,397,31,258,124,138,124,575,37,154,146,507,41,
%U A064946 544,43,351,325,186,47,892,105,392,190,413,53,692,192,693,212,234,59
%N A064946 a(n) = Sum_{i|n, j|n, j>i} j.
%H A064946 Harry J. Smith, <a href="/A064946/b064946.txt">Table of n, a(n) for n = 1..1000</a>
%F A064946 a(n) = Sum_{i=1..tau(n)} (i-1)*d_i, where {d_i}, i=1..tau(n), is the increasing sequence of the divisors of n.
%F A064946 a(n) = A064944(n) - A000203(n). - _Amiram Eldar_, Dec 23 2024
%F A064946 From _Ridouane Oudra_, Aug 06 2025: (Start)
%F A064946 a(n) = A064948(n) - A064944(n).
%F A064946 a(n) = A064840(n) - A064945(n).
%F A064946 a(n) = A337297(n) - A064947(n).
%F A064946 a(n) = (A064948(n) - A000203(n))/2. (End)
%e A064946 a(6) = dot_product(0,1,2,3)*(1,2,3,6) = 0*1 + 1*2 + 2*3 + 3*6 = 26.
%p A064946 with(numtheory): seq(add((i-1)*sort(convert(divisors(n),'list'))[i],i=1..tau(n)), n=1..200);
%t A064946 A064946[n_] := #.Range[Length[#]] & [Rest[Divisors[n]]];
%t A064946 Array[A064946, 100] (* _Paolo Xausa_, Aug 14 2025 *)
%o A064946 (PARI) a(n) = my(d=divisors(n)); sum(i=2, length(d), (i - 1)*d[i]); \\ _Harry J. Smith_, Oct 01 2009
%Y A064946 Cf. A064944, A064945, A064947, A064948, A064949.
%Y A064946 Cf. A000005, A000203, A064840, A337297, A027750.
%K A064946 nonn
%O A064946 1,2
%A A064946 _Vladeta Jovovic_, Oct 28 2001