[seqfan] Boris Stechkin and A055004

[israel at math.ubc.ca]

A055004 is titled "Boris Stechkin's function". It has a reference to R. K. 
Guy, Unsolved Problems Number Theory, A17. No formula is given, but 
according to the Maple code (which does match the Data) it would be

a(n) = Sum_{m=2..n} (m-1)*floor(n*(m-1)/m).

But this definition doesn't seem to match anything stated in A17 of 
"Unsolved Problems in Number Theory", which instead quotes three theorems 
of Boris Stechkin referring to the function

S(n) = # {m: 2 <= m <= n, (m-1) | floor(n(m-1)/m)}

For example, the first is that n-1 is prime iff S(n) = d(n), the number of
divisors of n.

This function S would produce (for 0 <= n <= 100) 0, 0, 1, 2, 3, 3, 4, 4, 
4, 5, 5, 4, 6, 6, 4, 6, 7, 5, 6, 6, 6, 8, 6, 4, 8, 9, 5, 6, 8, 6, 8, 8, 6, 
8, 6, 6, 11, 9, 4, 6, 10, 8, 8, 8, 6, 10, 8, 4, 10, 11, 7, 8, 8, 6, 8, 10, 
10, 10, 6, 4, 12, 12, 4, 8, 11, 9, 10, 8, 6, 8, 10, 8, 12, 12, 4, 8, 10, 8, 
10, 8, 10, 13, 7, 4, 12, 14, 6, 6, 10, 8, 12, 14, 8, 8, 6, 6, 14, 12, 6, 
10, 13

which does not seem to be in OEIS. I think it should be. But what to do 
about A055004? It's an old sequence, so we shouldn't change the Data. Is 
there a reference to this as a function of Stechkin? Does it have any 
relationship to be primes?

Cheers,
Robert