A037175 Numbers k such that |s(k) - k| = number of primes <= k, where s(k) is sigma(k) - k.

2, 3, 15, 22, 98, 460, 5408, 21170, 243568, 3587402, 25881424, 25888784, 33305870, 61202192, 115333190, 135135182, 167241932, 788355824, 788360176, 1653570248

Offset

1,1

Comments

a(21) > 10^11. - Donovan Johnson Aug 15 2011

Links

Table of n, a(n) for n=1..20.

Formula

{ k : abs(A033880(k)) = A000720(k) }.

Maple

with(numtheory):np:=0: for n from 1 to 300000 do if isprime(n) then np:=np+1 fi: if(abs(sigma(n)-2*n)=np) then printf("%d, ", n) fi od: # C. Ronaldo, Feb 20 2005
# Alternative:
q:= proc(k) uses numtheory; is(abs(sigma(k)-2*k)=pi(k)) end:
select(q, [$1..50000])[];  # Alois P. Heinz, Jun 17 2026

Prog

(PARI) np=0; for(n=1, 10000000, if(isprime(n), np=np+1); if(abs(sigma(n)-2*n)==np, print1(n, ", "))) \\ C. Ronaldo, Feb 20 2005

Crossrefs

Cf. A000203, A000720, A033880.

Sequence in context: A047176 A347668 A325236 * A048613 A162890 A030072

Adjacent sequences: A037172 A037173 A037174 * A037176 A037177 A037178

Keyword

nonn,more,changed

Author

Naohiro Nomoto

Extensions

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 30 2004

a(11)-a(20) from Donovan Johnson, Aug 15 2011

Status

approved