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A080101 Number of prime powers in all composite numbers between n-th prime and next prime. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The maximum value of terms in the sequence, through the 100,000th 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.

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: A185643 A278515 A285709 * A025895 A104451 A285680

Adjacent sequences:  A080098 A080099 A080100 * A080102 A080103 A080104

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jan 28 2003

STATUS

approved

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Last modified February 17 15:32 EST 2020. Contains 331998 sequences. (Running on oeis4.)