A181970 Places of nonprimes in A050376.

3, 6, 9, 13, 20, 28, 37, 47, 63, 71, 83, 111, 127, 160, 177, 235, 280, 301, 348, 377, 430, 509, 542, 633, 700, 731, 838, 875, 915, 1030, 1194, 1284, 1327, 1415, 1458, 1559, 1752, 1915, 2015, 2181, 2231, 2531, 2590, 2773, 2960, 3089, 3154, 3289, 3485, 3562, 3919, 3997, 4142

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

Crossrefs

Cf. A050376, A000040, A181962.

Sequence in context: A310161 A137041 A153006 * A316531 A242339 A086838

Adjacent sequences: A181967 A181968 A181969 * A181971 A181972 A181973

Keyword

nonn

Author

Vladimir Shevelev, Apr 06 2012

Extensions

a(30)-a(53) from Charles R Greathouse IV, Apr 10 2012

Status

approved