A280087 - OEIS

%I #17 Sep 08 2022 08:46:18

%S 14,1334,1634,2685,33998,42818,84134,122073,166934,289454,383594,

%T 440013,544334,605985,649154,655005,1642154,2284814,2913105,3571905,

%U 3682622,5181045,6771405,10074477,10195305,12825266,15751533,17714486,17727554,19886385,25096665,33422277,34577834,34883654

%N Numbers n such that Product_{d|n} sigma(d) = Product_{d|n+1} sigma(d).

%C sigma(n) is the sum of the divisors of n (A000203).

%C Numbers n such that A206032(n) = A206032(n+1).

%e 14 is a term because Product_{d|14} sigma(d) = 1 * 3 * 8 * 24 = Product_{d|15} sigma(d) = 1 * 4 * 6 * 24 = 576.

%t Select[Range[5000], Times @@ DivisorSigma[1, Divisors[#]] == Times @@ DivisorSigma[1, Divisors[# + 1]] &] (* _G. C. Greubel_, Dec 26 2016 *)

%o (Magma) [n: n in [1..1000] | &*[SumOfDivisors(d): d in Divisors(n)]  eq &*[SumOfDivisors(d): d in Divisors(n+1)]]

%o (PARI) isok(n) = my(d = divisors(n), dd = divisors(n+1)); prod(k=1, #d, sigma(d[k])) == prod(k=1, #dd, sigma(dd[k])); \\ _Michel Marcus_, Dec 26 2016

%Y Cf. A000203, A206032.

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Dec 25 2016

%E More terms from _Michel Marcus_, Dec 26 2016