

A125503


Smallest number k such that the numerator of generalized harmonic number H(k,n) = Sum[ 1/i^n, {i,1,k} ] is a prime.


1



2, 2, 3, 2, 23, 73, 15, 2, 3, 5, 13, 57, 3, 171, 5, 2, 21, 7, 55, 152, 26, 1298, 115, 139, 3, 2019, 3, 4, 3, 15, 56, 177
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OFFSET

1,1


COMMENTS

a(n) = 2 for n = {1,2,4,8,16,...}. Corresponding Fermat primes A019434 = {3, 5, 17, 257, 65537, ...}. a(n) = 3 for n = {3,9,13,25,27,29,95,107,153,159,...}. a(n) = 5 for n = {10,15,60,90,197,209,...}. a(n) = 7 for n = {18,47,112,155,273,...}. a(n) = 15 for n = {7,30,43,...}. a(28) = 4. a(31) = 56. a(144) = 9.
Contribution from Alexander Adamchuk, Apr 18 2010: (Start)
a(27)a(32) = {3,4,3,15,56,177}.
a(n) = 3 for all n>2 listed in A125706. (End)


LINKS

Table of n, a(n) for n=1..32.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics. Harmonic Number.


MATHEMATICA

Do[n = 1; f = 0; While[Not[PrimeQ[Numerator[f]]], f = f + 1/n^x; n++ ]; Print[{x, n  1}], {x, 1, 25}] [From Alexander Adamchuk, Apr 18 2010]


CROSSREFS

Cf. A001008, A007406, A007408, A007410, A099828.
Cf. A019434.
A125706. [From Alexander Adamchuk, Apr 18 2010]
Sequence in context: A283450 A297935 A127012 * A127009 A181313 A164089
Adjacent sequences: A125500 A125501 A125502 * A125504 A125505 A125506


KEYWORD

hard,more,nonn


AUTHOR

Alexander Adamchuk, Dec 28 2006, Jan 31 2007


EXTENSIONS

a(22)a(25) from Alexander Adamchuk, Apr 18 2010
a(26)a(32) from Alexander Adamchuk, Apr 26 2010


STATUS

approved



