cp's OEIS Frontend

A300906 Numbers k such that sigma(k)^k divides k^sigma(k).

%I A300906 #20 Apr 06 2025 19:55:46
%S A300906 1,6,28,84,120,364,420,496,672,840,1080,1320,1488,1782,2280,2760,3276,
%T A300906 3360,3472,3480,3720,3780,5640,7080,7392,7440,7560,8128,8736,9240,
%U A300906 9480,10416,10920,11880,12400,15456,15960,16368,16380,17880,18360,18600,19320,20520
%N A300906 Numbers k such that sigma(k)^k divides k^sigma(k).
%C A300906 Numbers k such that A217872(k) divides A100879(k).
%C A300906 Numbers k such that A300905(k) = 0.
%C A300906 Corresponding quotients: 1, 729, 123476695691247935826229781856256, ...
%C A300906 m-perfect numbers k (A007691) are terms iff m divides k.
%e A300906 6 is a term because 6^sigma(6) / sigma(6)^6 = 6^12 / 12^6 = 2176782336 / 2985984 = 729 (integer).
%p A300906 with(numtheory):
%p A300906 select(n->n &^ sigma(n) mod sigma(n)^n =0, [`$`(1..30000)]); # _Muniru A Asiru_, Mar 20 2018
%o A300906 (Magma) [n: n in[1..20000]  | n^SumOfDivisors(n) mod SumOfDivisors(n)^n eq 0];
%o A300906 (GAP) Filtered([1..30000],n->PowerModInt(n,Sigma(n),Sigma(n)^n)=0); # _Muniru A Asiru_, Mar 20 2018
%o A300906 (PARI) isok(n) = my(s = sigma(n)); Mod(n, s^n)^s == 0; \\ _Michel Marcus_, Mar 23 2018
%Y A300906 Cf. A000203, A100879, A217872, A300905.
%K A300906 nonn
%O A300906 1,2
%A A300906 _Jaroslav Krizek_, Mar 20 2018