A383269 a(n) is the smallest nonnegative solution to sigma(A383268(n) - x) + sigma(A383268(n) + x) = 4*A383268(n).

0, 1, 5, 11, 0, 7, 17, 28, 26, 37, 23, 14, 7, 13, 17, 49, 11, 22, 11, 5, 1, 58, 70, 13, 20, 37, 19, 11, 17, 31, 41, 67, 6, 16, 13, 73, 49, 11, 55, 91, 19, 73, 119, 5, 11, 77, 53, 43, 103, 86, 7, 114, 173, 88, 71, 59, 124, 95, 139, 7, 128, 31, 92, 143, 83, 227, 163

Offset: 1

Author

Felix Huber, Apr 24 2025

Keywords

• nonn
• easy

Examples

			a(2) = 1 because sigma(A383268(2) - 1) + sigma(A383268(2) + 1) =  sigma(13 - 1) + sigma(13 + 1) = sigma(12) + sigma(14) = 28 + 24 = 52 = 4*13 = 4*A383268(2).
		

Links

• Felix Huber, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Perfect Number

Crossrefs

Cf. A000203, A000396, A186103, A383268.

Programs

Maple

with(NumberTheory):
A383269:=proc(N) # To get the first N terms.
    local k,x,X;
    X:=[];
    for k while nops(X)A383269(67);

PARI

isok(k) = for (x=0, k-1, if (sigma(k - x) + sigma(k + x) == 4*k, return(x))); return(-1);
lista(nn) = for (n=1, nn, my(m=isok(n)); if (m != -1, print1(m, ", "))); \\ Michel Marcus, Apr 26 2025

Formula

a(n) = 0 iff A383268(n) is a perfect number (A000396) and vice versa.