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
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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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
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Mathematica
With[{r = Range[200]}, PositionIndex[CoprimeQ[r, Accumulate[DivisorSigma[0, r]]]][True]] (* Paolo Xausa, Feb 21 2024 *) -
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
Extensions
More terms from Max Alekseyev, May 10 2009
Comments