A304294 Numbers k having at least one divisor d such that sigma(k) = sigma(k+d).

14, 54, 154, 182, 206, 220, 238, 264, 266, 270, 284, 322, 366, 406, 434, 518, 574, 594, 602, 658, 660, 702, 742, 826, 834, 848, 852, 854, 918, 938, 957, 994, 1022, 1026, 1030, 1106, 1162, 1240, 1242, 1246, 1334, 1350, 1358, 1364, 1392, 1414, 1420, 1442, 1498, 1504

Offset

1,1

Comments

The first number that admits two different divisors is 702: two of its divisors are 6 and 26, and sigma(702) = sigma(702 + 6) = sigma(702 + 26) = 1680.

The first number that admits three different divisors is 11934: three of its divisors are 26, 102, and 442, and sigma(11934) = sigma(11934 + 26) = sigma(11934 + 102) = sigma(11934 + 442) = 30240.

Links

Table of n, a(n) for n=1..50.

Example

One divisor of 14 is 1 and sigma(14) = sigma(14 + 1) = 24.
One divisor of 54 is 2 and sigma(54) = sigma(54 + 2) = 120.

Maple

with(numtheory): P:=proc(n) local a, k, ok; a:=divisors(n); ok:=0;
for k from 1 to nops(a) do if sigma(n)=sigma(n+a[k]) then ok:=1; fi; od;
if ok=1 then n; fi; end: seq(P(i), i=1..1504);

Mathematica

Select[Range[2000], Function[k, AnyTrue[Divisors@ k, DivisorSigma[1, k] == DivisorSigma[1, k + #] &]]] (* Michael De Vlieger, May 14 2018 *)

Prog

(PARI) isok(n) = sumdiv(n, d, sigma(n+d) == sigma(n)) > 0; \\ Michel Marcus, May 14 2018

Crossrefs

Cf. A000203, A304295.

Sequence in context: A048971 A299646 A006597 * A114012 A140784 A022285

Adjacent sequences: A304291 A304292 A304293 * A304295 A304296 A304297

Keyword

nonn,easy

Author

Paolo P. Lava, May 14 2018

Status

approved