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A080101
Number of prime powers in all composite numbers between n-th prime and next prime.
19
0, 1, 0, 2, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0
OFFSET
1,4
COMMENTS
The maximum value of terms in the sequence, through the (10^5)th term, is 2. - Harvey P. Dale, Aug 24 2014
LINKS
EXAMPLE
There are two prime powers between 2179=A000040(327) and 2203=A000040(328): 2187=3^7 and 2197=13^3, therefore a(327)=2, A080102(327)=2187 and A080103(327)=2197.
MAPLE
a := proc(n) local c, k, p: c, p := 0, ithprime(n): for k from p+1 to nextprime(p)-1 do if nops(numtheory:-factorset(k)) = 1 then c := c+1: fi: od: c: end:
seq(a(n), n = 1 .. 105); # Lorenzo Sauras Altuzarra, Jul 08 2022
MATHEMATICA
prpwQ[n_]:=Module[{fi=FactorInteger[n]}, Length[fi]==1&&fi[[1, 2]]>1]; nn=600; With[{pwrs=Table[If[prpwQ[n], 1, 0], {n, nn}]}, Table[Total[ Take[ pwrs, {Prime[n], Prime[n+1]}]], {n, PrimePi[nn]-1}]] (* Harvey P. Dale, Aug 24 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jan 28 2003
STATUS
approved