A344765 - OEIS

%I #19 Jun 12 2021 06:05:37

%S 0,0,2,0,2,9,2,0,5,14,2,20,2,17,19,0,2,31,2,27,26,25,2,45,7,30,14,49,

%T 2,57,2,0,37,38,34,83,2,41,44,75,2,76,2,52,69,49,2,92,9,69,55,59,2,93,

%U 62,72,62,62,2,153,2,65,77,0,59,133,2,110,73,124,2,132,2,78,100,84,75,156,2,122,41,86,2,176,74,89

%N a(n) = sigma(n) - A011772(n).

%H Antti Karttunen, <a href="/A344765/b344765.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A344765/a344765.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = A000203(n) - A011772(n).

%F a(n) = A001065(n) + A344763(n).

%F a(n) = Sum_{d|n} A344768(d).

%F a(n) = A344769(n) - A294898(n).

%t A011772[n_] := Module[{m = 1}, While[Not[IntegerQ[m(m+1)/(2n)]], m++]; m];

%t a[n_] := DivisorSigma[1, n] - A011772[n];

%t Array[a, 100] (* _Jean-François Alcover_, Jun 12 2021 *)

%o (PARI) A344765(n) = (sigma(n) - A011772(n));

%Y Cf. A000203, A001065, A011772, A294898, A344763, A344766, A344768 (Möbius transform), A344769.

%K nonn

%O 1,3

%A _Antti Karttunen_, May 30 2021