A383268 Numbers k for which sigma(k - x) + sigma(k + x) = 4*k has at least one nonnegative solution.

6, 13, 15, 17, 28, 33, 39, 42, 50, 51, 53, 54, 55, 57, 59, 61, 65, 66, 69, 71, 77, 78, 82, 89, 90, 93, 95, 99, 101, 107, 111, 115, 118, 120, 121, 123, 125, 129, 131, 139, 141, 149, 153, 161, 165, 167, 171, 177, 179, 182, 183, 190, 195, 196, 197, 201, 204, 213, 215

Offset

1,1

Comments

Supersequence of A000396 because sigma(A000396(n) - x) + sigma(A000396(n) + x) = 4*A000396(n) has the solution x = 0.

Links

Michel Marcus, Table of n, a(n) for n = 1..10000 (terms up to n=1000 by Felix Huber).

Eric Weisstein's World of Mathematics, Perfect Number

Example

15 is in the sequence because sigma(15 - x) + sigma(15 + x) = 4*15 has the solution x = 5: sigma(15 - 5) + sigma(15 + 5) = sigma(10) + sigma(20) = 18 + 42 = 60 = 4*15.

Maple

with(NumberTheory):
A383268:=proc(N) # To get the first N terms.
    local k, x, K;
    K:=[];
    for k while nops(K)<N do
        for x from 0 to k-1 do
            if sigma(k-x)+sigma(k+x)=4*k then
                K:=[op(K), k];
                break
            fi
        od
    od;
    return op(K)
end proc;
A383268(59);

Prog

(PARI) isok(k) = for (x=0, k-1, if (sigma(k - x) + sigma(k + x) == 4*k, return(1))); \\ Michel Marcus, Apr 26 2025

Crossrefs

Cf. A000203, A000396, A186103, A383269.

Sequence in context: A100205 A353442 A140888 * A053753 A228380 A090068

Adjacent sequences: A383265 A383266 A383267 * A383269 A383270 A383271

Keyword

nonn,easy

Author

Felix Huber, Apr 24 2025

Status

approved