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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
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 A365430
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 March 19 01:57 EDT 2024. Contains 370952 sequences. (Running on oeis4.)