A280087 Numbers n such that Product_{d|n} sigma(d) = Product_{d|n+1} sigma(d).

14, 1334, 1634, 2685, 33998, 42818, 84134, 122073, 166934, 289454, 383594, 440013, 544334, 605985, 649154, 655005, 1642154, 2284814, 2913105, 3571905, 3682622, 5181045, 6771405, 10074477, 10195305, 12825266, 15751533, 17714486, 17727554, 19886385, 25096665, 33422277, 34577834, 34883654

Offset: 1

Author

Jaroslav Krizek, Dec 25 2016

Keywords

• nonn

Comments

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

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

Examples

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

Crossrefs

Cf. A000203, A206032.

Programs

Magma

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

Mathematica

Select[Range[5000], Times @@ DivisorSigma[1, Divisors[#]] == Times @@ DivisorSigma[1, Divisors[# + 1]] &] (* G. C. Greubel, Dec 26 2016 *)

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

Extensions

More terms from Michel Marcus, Dec 26 2016