A037176 - OEIS

A037176

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).

1, 2, 56, 80, 85, 2527, 2569, 2723, 2807, 7864, 7976, 22941, 113488, 174449, 461403, 1302379, 8513821, 14348051, 70110091, 70111621, 70112369, 249046528, 10910880311

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..23.

PROG

(PARI) us(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d));

f(n)=s=0; for(x=1, n, if(isprime(x), s++)); s;

for(n=1, 10^6, if(us(n)-n==f(n), print(n)));

(PARI) us(n) = {my(f=factor(n)); prod(k=1, #f~, f[k, 1]^f[k, 2]+1)-n}; \\ A034460

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

CROSSREFS

Cf. A000720, A034448, A034460.

Sequence in context: A278842 A307025 A376667 * A376851 A045819 A281198

Adjacent sequences: A037173 A037174 A037175 * A037177 A037178 A037179

KEYWORD

nonn

AUTHOR

Naohiro Nomoto

EXTENSIONS

a(12) from Jason Earls, Sep 06 2001

a(13)-a(15) from Nathaniel Johnston, Apr 29 2011

a(16)-a(22) from Donovan Johnson, Jul 24 2012

a(23) from Amiram Eldar, Jul 24 2024

STATUS

approved