Arnauld
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JavaScript (ES6)JavaScript (V8), 5063 bytes
Prints the sequence forever.
f={for(n=0;;s%t||print(n,k=n,t=s=0)=>k?f)for(n,k-1k=++n,t=s=0;k;)n%k?t:--||(s+=n,t+k)t-=~k):s%t<1}
JavaScript (V8), 63 bytes
Prints the sequence forever.
{for(n=0;;s%t||print(n))for(k=++n,t=s=0;k;)n%k--||(s+=n,t-=~k)}