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]
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
(Python)
from sympy import primepi, integer_nthroot, primefactors
def A095874(n): return 1+int(primepi(n)+sum(primepi(integer_nthroot(n, k)[0]) for k in range(2, n.bit_length()))) if n==1 or len(primefactors(n))==1 else 0 # Chai Wah Wu, Jan 19 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jun 10 2004
EXTENSIONS
Edited by M. F. Hasler, Jun 15 2021
STATUS
approved