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A323653 Multiperfect numbers m such that sigma(m) is also multiperfect. 1
1, 459818240, 51001180160, 13188979363639752997731839211623940096, 5157152737616023231698245840143799191339008, 54530444405217553992377326508106948362108928, 133821156044600922812153118065015159487725568, 4989680372093758991515359988337845750507257510078971904 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Multiperfect numbers m such that sigma(m) divides sigma(sigma(m)).

Also k-multiperfect numbers m such that k*m is also multiperfect.

Corresponding values of numbers k(n) = sigma(a(n)) / a(n): 1, 3, 3, 5, 5, 5, 5, 5, ...

Corresponding values of numbers h(n) = sigma(k(n) * a(n)) / (k(n) * a(n)): 1, 4, 4, 6, 6, 6, 6, 6, ...

Number of k-multiperfect numbers m such that sigma(n) is also multiperfect for k = 3..6: 2, 0, 20, 0.

Subsequence of A066961.

LINKS

Table of n, a(n) for n=1..8.

EXAMPLE

3-multiperfect number 459818240 is a term because number 3*459818240 = 1379454720 is a 4-multiperfect number.

PROG

(MAGMA) [n: n in [1..10^6] | SumOfDivisors(n) mod n eq 0 and SumOfDivisors(SumOfDivisors(n)) mod SumOfDivisors(n) eq 0]

(PARI) ismulti(n) = (sigma(n) % n) == 0;

isok(n) = ismulti(n) && ismulti(sigma(n)); \\ Michel Marcus, Jan 26 2019

CROSSREFS

Cf. A000396, A005820, A007691, A027687, A046060, A046061, A054030, A323652.

Sequence in context: A038830 A038819 A286846 * A246548 A260524 A091677

Adjacent sequences:  A323650 A323651 A323652 * A323654 A323655 A323656

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Jan 21 2019

STATUS

approved

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Last modified October 22 07:29 EDT 2019. Contains 328315 sequences. (Running on oeis4.)