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%I #25 Jul 24 2024 17:59:05
%S 1,2,56,80,85,2527,2569,2723,2807,7864,7976,22941,113488,174449,
%T 461403,1302379,8513821,14348051,70110091,70111621,70112369,249046528,
%U 10910880311
%N Numbers k such that us(k) = primepi(k), where us(k) is the sum of the aliquot unitary divisors of k (A034460), and primepi(k) is the number of primes <= k (A000720).
%o (PARI) us(n) = sumdiv(n,d, if(gcd(d,n/d)==1,d));
%o f(n)=s=0; for(x=1,n, if(isprime(x),s++)); s;
%o for(n=1,10^6, if(us(n)-n==f(n),print(n)));
%o (PARI) us(n) = {my(f=factor(n)); prod(k=1, #f~, f[k, 1]^f[k, 2]+1)-n}; \\ A034460
%o lista(pmax) = {my(prev = 2, k = 1); print1("1, 2, "); forprime(p = 3, pmax, for(c = prev + 1, p - 1, if(k == us(c), print1(c, ", "))); prev = p; k++);} \\ _Amiram Eldar_, Jul 24 2024
%Y Cf. A000720, A034448, A034460.
%K nonn
%O 1,2
%A _Naohiro Nomoto_
%E a(12) from _Jason Earls_, Sep 06 2001
%E a(13)-a(15) from _Nathaniel Johnston_, Apr 29 2011
%E a(16)-a(22) from _Donovan Johnson_, Jul 24 2012
%E a(23) from _Amiram Eldar_, Jul 24 2024
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