A378414 Sum of the integers from 1 to n that are not antidivisors of n.

1, 3, 4, 7, 10, 17, 18, 28, 37, 41, 54, 65, 72, 89, 102, 122, 125, 143, 172, 186, 209, 217, 242, 277, 286, 327, 336, 360, 411, 429, 454, 470, 513, 565, 578, 634, 653, 671, 728, 765, 820, 837, 890, 950, 949, 1023, 1068, 1120, 1153, 1195, 1284, 1284, 1343, 1433

Offset: 1

Author

Paolo P. Lava, Nov 25 2024

Keywords

• nonn
• easy

Comments

First two equal consecutive values for a(51) = a(52) = 1284.

Examples

			a(30) = 429 because 30*31/2 = 465, the antidivisors of 30 are 4, 12, 20 and 465 - 4 - 12 - 20 = 429.
		

Crossrefs

Cf. A000217, A024816, A066417.

Programs

Maple

with(numtheory): P:=proc(q) local j,k,n,v; v:=[1];
for n from 2 to q do k:=0; j:=n; while j mod 2<>1 do k:=k+1; j:=j/2; od;
v:=[op(v),n*(n+1)/2-(sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2)];
od; op(v); end: P(10^2);

Python

from sympy import divisor_sigma
def A378414(n): return 1 if n == 1 else (n*(n+13)>>1)+2-divisor_sigma((m:=n<<1)-1)-divisor_sigma(m+1)-(divisor_sigma(n>>(k:=(~n&n-1).bit_length()))<Chai Wah Wu, Dec 03 2024

Formula

a(n) = A000217(n) - A066417(n).