|
Search: id:A120271
|
|
|
| A120271 |
|
Numerator of Sum[ 1/(Prime[k]-1), {k,1,n}]. |
|
+0
8
|
|
| 1, 3, 7, 23, 121, 21, 173, 1597, 17927, 127469, 129317, 43619, 44081, 44521, 1033223, 13538159, 395369371, 132680013, 400467919, 402757063, 1214947859, 1221110939, 50305908619, 50529880549, 101470376303, 509322834499, 8691337402883
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
a(n) are square-free except for n=5,14,49,.. where squared prime factors are 11,211,479,...
a(n) divides A078456(n) = {1, 3, 14, 92, 968, 12096, 199296, 3679488, ...} = Number of numbers less than p(1)*p(2)*...*p(n) having exactly one prime factor among (p(1),p(2)....,p(n)) where p(n) is the n-th prime. The quotients are A078456(n)/a(n) = A135212(n) = {1, 1, 2, 4, 8, 576, 1152, 2304, 4608, 18432, 552960, ...}. - Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 23 2007
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics. Prime Sums.
|
|
FORMULA
|
a(n) = numerator[ Sum[ 1/(Prime[k]-1), {k,1,n}]].
|
|
MATHEMATICA
|
Numerator[Table[Sum[1/(Prime[i]-1), {i, 1, n}], {n, 1, 50}]]
|
|
CROSSREFS
|
Cf. A119686, A006093, A000040.
Cf. A135212, A078456.
Adjacent sequences: A120268 A120269 A120270 this_sequence A120272 A120273 A120274
Sequence in context: A080077 A096318 A133788 this_sequence A048721 A113824 A121883
|
|
KEYWORD
|
frac,nonn
|
|
AUTHOR
|
Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 01 2006
|
|
|
Search completed in 0.002 seconds
|
