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A280087 Numbers n such that Product_{d|n} sigma(d) = Product_{d|n+1} sigma(d). 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

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

LINKS

Table of n, a(n) for n=1..34.

EXAMPLE

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

MATHEMATICA

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

PROG

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

(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

CROSSREFS

Cf. A000203, A206032.

Sequence in context: A137603 A160107 A054004 * A240703 A240640 A204698

Adjacent sequences:  A280084 A280085 A280086 * A280088 A280089 A280090

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Dec 25 2016

EXTENSIONS

More terms from Michel Marcus, Dec 26 2016

STATUS

approved

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Last modified July 24 03:48 EDT 2017. Contains 289717 sequences.