|
Search: id:A030059
|
|
|
| A030059 |
|
Numbers that are the product of an odd number of distinct primes. |
|
+0
8
|
|
| 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 30, 31, 37, 41, 42, 43, 47, 53, 59, 61, 66, 67, 70, 71, 73, 78, 79, 83, 89, 97, 101, 102, 103, 105, 107, 109, 110, 113, 114, 127, 130, 131, 137, 138, 139, 149, 151, 154, 157, 163, 165, 167, 170, 173, 174, 179, 181, 182, 186, 190, 191, 193
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
REFERENCES
|
Ramanujan, Collected Papers, pp. xxiv, 21.
B. C. Berndt & R. A. Rankin, Ramanujan: Letters and Commentary, see p. 23; AMS Providence RI 1995.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=1..1000
S. Ramanujan, Irregular numbers, J. Indian Math. Soc. 5 (1913) 105-106.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Moebius Function
Eric Weisstein's World of Mathematics, Prime Sums
|
|
FORMULA
|
omega(a(n)) = A001221(a(n)) gives A005408. {primes A000040} UNION {sphenic numbers A007304} UNION {numbers that are divisible by exactly 5 different primes A051270} UNION {products of 7 distinct primes (square-free 7-almost primes) A123321} UNION {products of 9 distinct primes; also n has exactly 9 distinct prime factors and n is square-free A115343} UNION.... - Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 19 2007
|
|
MAPLE
|
a := n -> `if`(numtheory[mobius](n)=-1, n, NULL); seq(a(i), i=1..193); [From Peter Luschny (peter(AT)luschny.de), May 04 2009]
|
|
CROSSREFS
|
Cf. A000040, A001221, A005408, A007304, A030231, A051270, A123321.
Sequence in context: A079603 A095959 A028905 this_sequence A089063 A117095 A054403
Adjacent sequences: A030056 A030057 A030058 this_sequence A030060 A030061 A030062
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
More terms from David W. Wilson (davidwwilson(AT)comcast.net)
|
|
|
Search completed in 0.002 seconds
|
