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

1,2

Comments

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

Links

Table of n, a(n) for n=1..54.

Formula

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

Example

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

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);

Prog

(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()))<<k+1) # Chai Wah Wu, Dec 03 2024

Crossrefs

Cf. A000217, A024816, A066417.

Sequence in context: A047967 A282893 A256912 * A134591 A058611 A357459

Adjacent sequences: A378411 A378412 A378413 * A378415 A378416 A378417

Keyword

nonn,easy

Author

Paolo P. Lava, Nov 25 2024

Status

approved