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 A095874 a(n) = k if n = A000961(k) (powers of primes), a(n) = 0 if n is not in A000961. 21
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA a(n) = Sum_{1 <= k <= n} A010055(k); [corrected by M. F. Hasler, Jun 15 2021] a(n) = A065515(n)*(A065515(n)-A065515(n-1)). a(n) = A065515(n)*A069513(n). - M. F. Hasler, Jun 16 2021 MATHEMATICA Join[{1}, Module[{k=2}, Table[If[PrimePowerQ[n], k; k++, 0], {n, 2, 100}]]] (* Harvey P. Dale, Aug 15 2020 *) PROG (Haskell) a095874 n | y == n    = length xs + 1           | otherwise = 0           where (xs, y:ys) = span (< n) a000961_list -- Reinhard Zumkeller, Feb 16 2012, Jun 26 2011 (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 CROSSREFS Cf. A000961 (right inverse), A049084, A097621. Sequence in context: A257846 A203572 A195829 * A279385 A267000 A224892 Adjacent sequences:  A095871 A095872 A095873 * A095875 A095876 A095877 KEYWORD nonn AUTHOR Reinhard Zumkeller, Jun 10 2004 EXTENSIONS Edited by M. F. Hasler, Jun 15 2021 STATUS approved

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Last modified June 29 10:17 EDT 2022. Contains 354913 sequences. (Running on oeis4.)