|
Search: id:A133364
|
|
|
| A133364 |
|
Number of ways of writing n as a sum of a prime and a square-full number. |
|
+0
1
|
|
| 1, 1, 0, 2, 1, 1, 1, 1, 3, 2, 1, 2, 2, 1, 1, 2, 2, 2, 3, 1, 2, 1, 1, 1, 4, 2, 2, 3, 1, 4, 2, 2, 3, 1, 2, 5, 4, 2, 2, 2, 2, 3, 4, 2, 3, 2, 3, 2, 4, 2, 2, 3, 3, 4, 2, 1, 2, 2, 2, 4, 3, 1, 2, 3, 3, 5, 4, 2, 2, 3, 2, 3, 6, 1, 5, 2, 4, 4, 2, 1, 6, 3, 2, 4, 4, 3, 3, 2
(list; graph; listen)
|
|
|
OFFSET
|
3,4
|
|
|
COMMENT
|
This is to square-full numbers A001694 as A098983 is to square-free numbers A005117 and as A002471 is to squares A000290. Asymptotics of this should relate to A098983.
|
|
FORMULA
|
a(n) = Card{n = i + j where i is in A000040 and j is in A001694}.
|
|
EXAMPLE
|
a(3) = 1 because 3=2+1 where 2 is prime and 1 is square-full.
a(4) = 1 because 4=3+1 where 3 is prime and 1 is square-full.
a(5) = 0 because there is no positive solution to 5 = prime+(square-full).
a(6) = 2 because 6=5+1=2+4.
a(7) = 1 because 7=3+4.
a(8) = 1 because 8=7+1.
a(9) = 1 because 9=5+4.
a(10) = 1 because 10=2+8.
a(11) = 3 because 11=2+9=3+8=7+4.
a(12) = 2 because 12=3+9=11+1.
a(13) = 1 because 13=5+8.
a(14) = 2 because 14=5+9=13+1.
a(15) = 2 because 15=7+8=11+4.
a(16) = 1 because 16=7+9.
a(17) = 1 because 17=13+4.
a(18) = 2 because 18=2+16=17+1.
a(19) = 2 because 19=3+16=11+8.
a(20) = 2 because 20=19+1=11+9.
|
|
MAPLE
|
isA001694 := proc(n) local digs, i ; digs := ifactors(n)[2] ; for i in digs do if op(2, i) = 1 then RETURN(false) ; fi ; od: RETURN(true) ; end: A133364 := proc(n) local a, p ; a := 0 ; p := 2 ; while p < n do if isA001694(n-p) then a := a+1 ; fi ; p := nextprime(p) ; od: RETURN(a) ; end: seq(A133364(n), n=3..90) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 09 2007
|
|
MATHEMATICA
|
a = {}; For[n = 3, n < 100, n++, c = 0; For[j = 1, Prime[j] < n, j++, d = 1; b = FactorInteger[n - Prime[j]]; For[m = 1, m < Length[b] + 1, m++, If[b[[m, 2]] < 2, d = 0]]; If[d == 1, c++ ]]; AppendTo[a, c]]; a - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Oct 29 2007
|
|
CROSSREFS
|
Cf. A000040, A000290, A001694, A002471, A005117, A098983.
Sequence in context: A030358 A118914 A124010 this_sequence A063420 A029385 A026536
Adjacent sequences: A133361 A133362 A133363 this_sequence A133365 A133366 A133367
|
|
KEYWORD
|
easy,more,nonn
|
|
AUTHOR
|
Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 26 2007
|
|
EXTENSIONS
|
Corrected and extended by Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Oct 29 2007 and by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 09 2007
|
|
|
Search completed in 0.002 seconds
|
