login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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