A135484
a(n) = Sum_{i=1..n} i^prime(i), where prime(i) denotes i-th prime number.
Original entry on oeis.org
1, 9, 252, 16636, 48844761, 13109538777, 232643623525984, 144347831699381856, 8863082467484200477785, 100000008863082467484200477785, 192043424966613562971631041769596
Offset: 1
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f[n_] := Sum[i^Prime@i, {i, n}]; Array[f, 12] (* Robert G. Wilson v, Feb 12 2008 *)
Accumulate[Table[n^Prime[n],{n,15}]] (* Harvey P. Dale, Nov 30 2023 *)
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a(n) = sum(k=1, n, k^prime(k)); \\ Michel Marcus, Oct 15 2016
A135485
a(n) = Sum_{i=1..n} prime(i)^(i-1), where prime(i) denotes i-th prime number.
Original entry on oeis.org
1, 4, 29, 372, 15013, 386306, 24523875, 918395614, 79229380895, 14586375356764, 834214662337565, 178751836441797978, 22742242136807984059, 1741006366419098769302, 258407992554086508103671
Offset: 1
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f[n_] := Sum[Prime[i]^(i - 1), {i, n}]; Array[f, 16] (* Robert G. Wilson v, Feb 12 2008 *)
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a(n) = sum(k=1, n, prime(k)^(k-1)); \\ Michel Marcus, Oct 15 2016
A291140
Sum of the n-th powers of the first n primes.
Original entry on oeis.org
2, 13, 160, 3123, 181258, 6732437, 493478344, 24995572327, 2255433009730, 470444892889497, 38714638073629150, 7749166585021832891, 1203906832960860262108, 121893712541593098356317, 17161342484454585041813494
Offset: 1
a(3) = 2^3 + 3^3 + 5^3 = 160.
A298883
Determinant of n X n matrix whose elements are m(i,j) = prime(i)^j.
Original entry on oeis.org
1, 2, 6, 180, 50400, 958003200, 131514679296000, 1352181326649753600000, 112703642894318944282214400000, 903025586371469323704949549301760000000, 2012769637740033870687308804001121075357286400000000
Offset: 0
For n=1:
|2| = 2, then a(1) = 2.
For n=2:
|2 4| = 6, then a(2) = 6.
|3 9|
For n=3:
|2 4 8| = 180, then a(3) = 180.
|3 9 27|
|5 25 125|
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with(LinearAlgebra):
a:= n-> Determinant(Matrix(n, (i,j)-> ithprime(i)^j)):
seq(a(n), n=0..12); # Alois P. Heinz, Jan 28 2018
# Alternative:
f:= proc(n) local P;
P:= [seq(ithprime(i),i=1..n)];
convert(P,`*`)*mul(mul(P[j]-P[i],j=i+1..n),i=1..n-1)
end proc:
map(f, [$0..20]); # Robert Israel, Jan 29 2018
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a[n_]:=Table[Prime[i]^j,{i,1,n},{j,1,n}];
Table[Det[a[n]],{n,1,10}]
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a(n) = matdet(matrix(n, n, i, j, prime(i)^j)); \\ Michel Marcus, Jan 28 2018
A179056
Numbers k such that prime(1)^1 + prime(2)^2 + ... + prime(k)^k is prime.
Original entry on oeis.org
prime(1)^1 + prime(2)^2 + ... + prime(8)^8 = 17398892111 is prime, so 8 is in the sequence.
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Select[Range[1, 100], PrimeQ[Sum[Prime[i]^i, {i, 1, #}]] &] (* Julien Kluge, Dec 03 2016 *)
Showing 1-5 of 5 results.
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