A247939
Sum of divisors of 2^prime(n)+1.
Original entry on oeis.org
6, 13, 48, 176, 2736, 10928, 174768, 699056, 11184816, 727960800, 2863311536, 183355069408, 2967356682528, 11728124029616, 188313058624992, 12121838249371488, 768906329487027264, 3074457345618258608, 196765296972010592800, 3148244377723715041632
Offset: 1
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[SumOfDivisors(2^p+1): p in PrimesUpTo(100)];
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with(numtheory): A247939:=n->sigma(2^ithprime(n)+1): seq(A247939(n), n=1..20); # Wesley Ivan Hurt, Sep 27 2014
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Table[DivisorSigma[1, 2^Prime[n] + 1], {n, 1, 20}]
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vector(50,n,sigma(2^prime(n)+1)) \\ Derek Orr, Sep 27 2014
A268130
Primes p of the form sigma(2^k + 1) - 1 for some k >= 0.
Original entry on oeis.org
2, 3, 5, 17, 47, 83, 257, 1301, 65537, 174767, 5048231, 51322664447, 188313058624991, 4768522825659911, 3148244377723715041631, 211635519858089932125000235391, 906780938207203620571208267879698943, 6392739029893008727817055462596999999
Offset: 1
Prime 47 is a term because for k = 5, sigma(2^5+1) - 1 = sigma(33) - 1 = 47.
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Set(Sort([SumOfDivisors(2^n+1)-1: n in [0..300] | IsPrime(SumOfDivisors(2^n+1)-1)]));
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lista(nn) = for (n=0, nn, if (isprime(p=sigma(2^n + 1) - 1), print1(p, ", "))); \\ Michel Marcus, Jan 27 2016
A334876
Numbers m with the property that sigma(2^m+1)/(2^m+1) > sigma(2^k+1)/(2^k+1) for all k < m, where sigma is the sum of divisors function, A000203.
Original entry on oeis.org
1, 3, 5, 9, 15, 45, 135, 315, 945
Offset: 1
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r[n_] := DivisorSigma[1, 2^n+1]/(2^n + 1); seq = {}; rm = 1; Do[r1 = r[n]; If[r1 > rm, rm = r1; AppendTo[seq, n]], {n, 1, 50}]; seq (* Amiram Eldar, May 15 2020 *)
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def h(n):
return (sigma(n,1))/n
def hchecker(k):
s=0
for i in range(1,k):
j=2^i+1
a=h(j)
if a> s:
print(i)
s=a
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