|
Search: id:A056924
|
|
|
| A056924 |
|
Number of divisors of n that are smaller than sqrt(n). |
|
+0
6
|
|
| 0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 2, 3, 1, 4, 1, 3, 2, 2, 2, 4, 1, 2, 2, 4, 1, 4, 1, 3, 3, 2, 1, 5, 1, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 6, 1, 2, 3, 3, 2, 4, 1, 3, 2, 4, 1, 6, 1, 2, 3, 3, 2, 4, 1, 5, 2, 2, 1, 6, 2, 2, 2, 4, 1, 6, 2, 3, 2, 2, 2, 6, 1, 3, 3, 4, 1, 4, 1, 4, 4
(list; graph; listen)
|
|
|
OFFSET
|
1,6
|
|
|
COMMENT
|
Number of powers of n in product of factors of n if n>1.
If n is a prime or the square of a prime, then a(n)=1.
|
|
FORMULA
|
For n>1, a(n) = floor[log(A007955(n))/log(n)] = log(A056925(n))/log(n) = floor[d(n)/2] = floor[A000005(n)/2].
a(n)=A000005[n]-A038548[n]. - Labos E. (labos(AT)ana.sote.hu), Apr 19 2002
G.f.: Sum_{k>0} x^(k^2+k)/(1-x^k) . - Michael Somos Mar 18 2006
|
|
EXAMPLE
|
a(16)=2 since the factors of 16 are 1,2,4,8,16 and their product is 1024=8*16^2
n=96: a(96)=Card[{1,2,3,4,6,8}]=6=Card[{12,16,24,32,48,96}]; n=225: a(225)=Card[{1,3,5,9}]=Card[{15,25,45,7,225}]-1 - Labos E. (labos(AT)ana.sote.hu), Apr 19 2002
|
|
MATHEMATICA
|
di[x_] := Divisors[x] lds[x_] := Ceiling[DivisorSigma[0, x]/2] rd[x_] := Reverse[Divisors[x]] td[x_] := Table[Part[rd[x], w], {w, 1, lds[x]}] sud[x_] := Apply[Plus, td[x]] Table[DivisorSigma[0, w]-lds[w], {w, 1, 128}] - Labos E. (labos(AT)ana.sote.hu), Apr 19 2002
|
|
PROGRAM
|
(PARI) a(n)=if(n<1, 0, numdiv(n)\2) /* Michael Somos Mar 18 2006 */
|
|
CROSSREFS
|
Cf. A038548, A000203, A000005, A070038, A070039.
Sequence in context: A087942 A099042 A140774 this_sequence A045778 A033103 A060775
Adjacent sequences: A056921 A056922 A056923 this_sequence A056925 A056926 A056927
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Henry Bottomley (se16(AT)btinternet.com), Jul 12 2000
|
|
EXTENSIONS
|
Edited by Michael Somos, Mar 18 2006
|
|
|
Search completed in 0.002 seconds
|
