A140221 A number n is included if n is coprime to Sum_{k=1..n} d(k), where d(k) is the number of divisors of k.

1, 2, 3, 7, 9, 10, 11, 12, 13, 14, 17, 19, 23, 25, 27, 28, 29, 31, 32, 34, 35, 37, 41, 43, 45, 49, 50, 51, 52, 53, 54, 56, 58, 59, 61, 62, 65, 67, 69, 71, 73, 75, 77, 79, 81, 82, 83, 84, 86, 87, 88, 89, 92, 93, 94, 95, 97, 98, 101, 103, 107, 109, 111, 113, 115, 117, 119, 122

Offset

1,2

Comments

Sum_{k=1..n} d(k) = Sum_{k=1..n} floor(n/k) = A006218(n).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

N:= 500: # for terms <= N
S:= ListTools:-PartialSums(map(numtheory:-tau, [$1..N])):
select(t -> igcd(t, S[t])=1, [$1..N]); # Robert Israel, Feb 20 2024

Mathematica

With[{r = Range[200]}, PositionIndex[CoprimeQ[r, Accumulate[DivisorSigma[0, r]]]][True]] (* Paolo Xausa, Feb 21 2024 *)

Prog

(Python)
from math import gcd, isqrt
def A140221_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n: gcd(n, -(s:=isqrt(n))**2+(sum(n//k for k in range(1, s+1))<<1))==1, count(max(startvalue, 1)))
A140221_list = list(islice(A140221_gen(), 30)) # Chai Wah Wu, Oct 23 2023

Crossrefs

Cf. A006218, A050226, A140222.

Sequence in context: A168222 A323384 A349641 * A046668 A047533 A060525

Adjacent sequences: A140218 A140219 A140220 * A140222 A140223 A140224

Keyword

nonn

Author

Leroy Quet, May 12 2008

Extensions

More terms from Max Alekseyev, May 10 2009

Status

approved