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.
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
KEYWORD
nonn,easy
AUTHOR
Paolo P. Lava, May 14 2018
STATUS
approved