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A095874
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a(n) = k if n = A000961(k) (powers of primes), a(n) = 0 if n is not in A000961.
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21
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1, 2, 3, 4, 5, 0, 6, 7, 8, 0, 9, 0, 10, 0, 0, 11, 12, 0, 13, 0, 0, 0, 14, 0, 15, 0, 16, 0, 17, 0, 18, 19, 0, 0, 0, 0, 20, 0, 0, 0, 21, 0, 22, 0, 0, 0, 23, 0, 24, 0, 0, 0, 25, 0, 0, 0, 0, 0, 26, 0, 27, 0, 0, 28, 0, 0, 29, 0, 0, 0, 30, 0, 31, 0, 0, 0, 0, 0, 32, 0, 33, 0, 34, 0, 0, 0, 0, 0, 35, 0
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OFFSET
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1,2
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COMMENTS
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The name has been edited to clarify that the indices k refer to A000961 ("powers of primes" = {1} U A246655) and not to the list A246655 of proper prime powers. - M. F. Hasler, Jun 16 2021
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LINKS
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FORMULA
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MATHEMATICA
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Join[{1}, Module[{k=2}, Table[If[PrimePowerQ[n], k; k++, 0], {n, 2, 100}]]] (* Harvey P. Dale, Aug 15 2020 *)
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PROG
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(Haskell)
a095874 n | y == n = length xs + 1
| otherwise = 0
where (xs, y:ys) = span (< n) a000961_list
(PARI) a(n)=if(isprimepower(n), sum(i=1, logint(n, 2), primepi(sqrtnint(n, i)))+1, n==1) \\ Charles R Greathouse IV, Apr 29 2015
(PARI) {M95874=Map(); A095874(n, k)=if(mapisdefined(M95874, n, &k), k, isprimepower(n), mapput(M95874, n, k=sum(i=1, exponent(n), primepi(sqrtnint(n, i)))+1); k, n==1)} \\ Variant with memoization, possibly useful to compute A097621, A344826 and related. One may omit "isprimepower(n), " (possibly requiring factorization) and ", n==1" if n is known to be a power of a prime, i.e., to get a left inverse for A000961. - M. F. Hasler, Jun 15 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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