A080101 Number of prime powers in all composite numbers between n-th prime and next prime.

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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Cf. A080102, A080103, A025475, A000961.

Sequence in context: A363051 A278515 A285709 * A025895 A104451 A285680

Adjacent sequences: A080098 A080099 A080100 * A080102 A080103 A080104

Keyword

nonn

Author

Reinhard Zumkeller, Jan 28 2003

Status

approved