cp's OEIS Frontend

A139247 Triangle read by rows: row n lists the divisors of n-th perfect number A000396(n) that are multiples of n-th Mersenne prime A000668(n).

%I A139247 #7 Sep 27 2024 05:42:37
%S A139247 3,6,7,14,28,31,62,124,248,496,127,254,508,1016,2032,4064,8128,8191,
%T A139247 16382,32764,65528,131056,262112,524224,1048448,2096896,4193792,
%U A139247 8387584,16775168,33550336,131071,262142,524284,1048568,2097136,4193792
%N A139247 Triangle read by rows: row n lists the divisors of n-th perfect number A000396(n) that are multiples of n-th Mersenne prime A000668(n).
%C A139247 Also, row n list the divisors of n-th perfect number that are not powers of 2.
%C A139247 First term of row n is the n-th Mersenne prime A000668(n). Last term of row n is the n-th perfect number A000396(n). Row n has A000043(n) terms. The sum of row n is equal to A133049(n), the square of n-th Mersenne prime A000668(n).
%H A139247 Omar E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>.
%e A139247 Triangle begins:
%e A139247   3, 6,
%e A139247   7, 14, 28
%e A139247   31, 62, 124, 248, 496
%e A139247   127, 254, 508, 1016, 2032, 4064, 8128
%e A139247   ...
%e A139247 ==========================================================
%e A139247 Row .... First term ..... Last term ....... Row sum ......
%e A139247 n ..... (A000668(n)) ... (A000396(n)) ... (A000668(n)^2) .
%e A139247 ==========================================================
%e A139247 1 ............ 3 .............. 6 ......... 3^2 = 9
%e A139247 2 ............ 7 ............. 28 ......... 7^2 = 49
%e A139247 3 ........... 31 ............ 496 ........ 31^2 = 961
%e A139247 4 .......... 127 ........... 8128 ....... 127^2 = 16129
%e A139247 5 ......... 8191 ....... 33550336 ...... 8191^2 = 67092481
%Y A139247 Cf. A000043, A000396, A000668, A018254, A018487, A133024, A133025, A133031, A133049, A135652, A135653, A135654, A135655.
%K A139247 nonn,tabf
%O A139247 1,1
%A A139247 _Omar E. Pol_, Apr 22 2008