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A181970 Places of nonprimes in A050376. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 15 01:25 EDT 2021. Contains 343909 sequences. (Running on oeis4.)