A152921
a(n) = 2^(2p-1)/2, where p is A000043(n).
Original entry on oeis.org
4, 16, 256, 4096, 16777216, 4294967296, 68719476736, 1152921504606846976, 1329227995784915872903807060280344576, 95780971304118053647396689196894323976171195136475136, 6582018229284824168619876730229402019930943462534319453394436096
Offset: 1
A152923
a(n) = 2^(2*p-1)/8, where p is A000043(n).
Original entry on oeis.org
1, 4, 64, 1024, 4194304, 1073741824, 17179869184, 288230376151711744, 332306998946228968225951765070086144, 23945242826029513411849172299223580994042798784118784, 1645504557321206042154969182557350504982735865633579863348609024
Offset: 1
A330841
Numbers of the form 2^(2*p-3)*9*M_p^2, where p > 2 is a Mersenne exponent, A000043, and M_p is the corresponding Mersenne prime, A000668.
Original entry on oeis.org
3528, 1107072, 297289728, 5065312705708032, 332036326796518490112, 85002272432789680816128, 23926103901845565010319828907592777728, 31803247166010917904914435277786533840425989636087697369118739195223867392
Offset: 1
a(2) = 2^(2*5-3)*9*31^2 = 2^7*9*31^2 = 1107072 has spectral basis {1023^2, 496^2, 960^2}, consisting of powers. The spectral sum of a(2), that is, the sum of the elements of its spectral basis, is 2*a(2)+1 = 2214145. In this case we say that a(2) has index 2. The number 9 * A330817(2) = 2^(2*5-2)*9*31^2 = 2^8*9*31^2 = 2214144 has the same spectral basis as a(2), but with index 1. We say that 9 * A330817(2) and a(2) are isospectral and form an isospectral pair.
Cf.
A000043,
A000668,
A133049,
A133051,
A152921,
A152922,
A330818,
A330819,
A330820, 9*
A133051, 9*
A330817,
A330837.
-
a := proc(n::posint)
local p, m;
p:=NumberTheory[IthMersenne](n+1);
m:=2^p-1;
return 2^(2*p-3)*9*m^2;
end;
-
f[p_] := 9*2^(2*p - 3)*(2^p - 1)^2; f /@ MersennePrimeExponent /@ Range[2, 9] (* Amiram Eldar, Feb 07 2020 *)
Showing 1-3 of 3 results.
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