A140237 A number n is included if (Sum_{k=1..n} d(k)) is divisible by d(n), where d(n) is the number of positive divisors of n.

1, 5, 7, 8, 16, 17, 19, 20, 23, 25, 37, 41, 42, 43, 47, 49, 64, 65, 67, 68, 69, 70, 71, 73, 74, 77, 79, 101, 103, 107, 108, 109, 113, 149, 150, 151, 155, 157, 163, 164, 165, 166, 167, 169, 197, 199, 211, 223, 257, 259, 263, 264, 265, 267, 268, 269, 271, 274, 275, 277

Offset

1,2

Comments

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

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Mathematica

s = 0; Reap[Do[If[Divisible[s += #, #], Sow[i]] &[DivisorSigma[0, i]], {i, 280}] ][[-1, 1]] (* Michael De Vlieger, Oct 23 2023 *)

Prog

(Python)
from math import isqrt
from sympy import divisor_count
def A140237_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n: not (-(s:=isqrt(n))**2+(sum(n//k for k in range(1, s+1))<<1))%divisor_count(n), count(max(startvalue, 1)))
A140237_list = list(islice(A140237_gen(), 30)) # Chai Wah Wu, Oct 23 2023

Crossrefs

Cf. A000005, A006218, A140238.

Sequence in context: A242408 A171952 A238011 * A032683 A182005 A192285

Adjacent sequences: A140234 A140235 A140236 * A140238 A140239 A140240

Keyword

nonn

Author

Leroy Quet, May 14 2008

Extensions

Extended by Ray Chandler, Jun 25 2009

Status

approved