OFFSET
1,1
COMMENTS
Or numbers not expressed in the form pi(p) + pi(sqrt(p)) + pi((sqrt(sqrt(p)))) +... with prime p.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
a(n) ~ 0.5 n^2 log n. - Charles R Greathouse IV, Apr 11 2012
EXAMPLE
Show that 28 not expressed in form pi(p) + pi(sqrt(p)) + pi((sqrt(sqrt(p)))) +... with prime p. Indeed, for p=79, this sum is 22+4+1=27, while for p=83, it is 23+4+2=29.
PROG
(PARI) first_few(lim)=my(v=List(apply(n->n^2, primes(primepi(sqrtint(lim))))), u, t); forprime(p=2, (lim+.5)^(1/4), t=p^2; while((t=t^2)<=lim, listput(v, t))); listput(v, 1); v=vecsort(Vec(v)); u=vector(#v-1, i, sum(j=v[i]+1, v[i+1]-1, isprime(j))); u[1]++; for(i=2, #u, u[i]+=u[i-1]+1); u \\ Charles R Greathouse IV, Apr 10 2012
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Apr 06 2012
EXTENSIONS
a(30)-a(53) from Charles R Greathouse IV, Apr 10 2012
STATUS
approved