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A300906 Numbers k such that sigma(k)^k divides k^sigma(k). 3
1, 6, 28, 84, 120, 364, 420, 496, 672, 840, 1080, 1320, 1488, 1782, 2280, 2760, 3276, 3360, 3472, 3480, 3720, 3780, 5640, 7080, 7392, 7440, 7560, 8128, 8736, 9240, 9480, 10416, 10920, 11880, 12400, 15456, 15960, 16368, 16380, 17880, 18360, 18600, 19320, 20520 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers k such that A217872(k) divides A100879(k).

Numbers k such that A300905(k) = 0.

Corresponding quotients: 1, 729, 123476695691247935826229781856256, ...

m-perfect numbers k (A007691) are terms iff m divides k.

LINKS

Table of n, a(n) for n=1..44.

EXAMPLE

6 is a term because 6^sigma(6) / sigma(6)^6 = 6^12 / 12^6 = 2176782336 / 2985984 = 729 (integer).

MAPLE

with(numtheory):

select(n->n &^ sigma(n) mod sigma(n)^n =0, [`$`(1..30000)]); # Muniru A Asiru, Mar 20 2018

PROG

(MAGMA) [n: n in[1..20000]  | n^SumOfDivisors(n) mod SumOfDivisors(n)^n eq 0]

(GAP) Filtered([1..30000], n->PowerModInt(n, Sigma(n), Sigma(n)^n)=0); # Muniru A Asiru, Mar 20 2018

(PARI) isok(n) = my(s = sigma(n)); Mod(n, s^n)^s == 0; \\ Michel Marcus, Mar 23 2018

CROSSREFS

Cf. A000203, A100879, A217872, A300905.

Sequence in context: A308585 A202956 A279915 * A222198 A302650 A055711

Adjacent sequences:  A300903 A300904 A300905 * A300907 A300908 A300909

KEYWORD

nonn,changed

AUTHOR

Jaroslav Krizek, Mar 20 2018

STATUS

approved

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Last modified October 15 17:35 EDT 2021. Contains 348033 sequences. (Running on oeis4.)