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

Author

Felix Huber, Apr 24 2025

Keywords

• nonn
• easy

Comments

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

Examples

			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.
		

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

Crossrefs

Cf. A000203, A000396, A186103, A383269.

Programs

Maple

with(NumberTheory):
A383268:=proc(N) # To get the first N terms.
    local k,x,K;
    K:=[];
    for k while nops(K)A383268(59);

PARI

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