Positive Totient function? We know that:
$$\phi(n) = n(1- 1/p_1)(1-1/p_2)\ldots(1 - 1/p_k)$$
where $\phi$ is the Euler totient function and $p_i$ are the primes dividing $n$.
Is anything known about the similar function
$$\varphi(n)= n(1+1/p_1)(1+1/p_2)\ldots (1+1/p_k)?$$
I'm just looking reading material and references. Does it have a name?
 A: Next time you have a similar question, you can try to put the few starting values into the search bar on OEIS.org. In this case, you would've found your answer. (Sometimes it is useful to omit the first value due to different conventions, e.g. here the empty product is taken to be $1$.)

From wikipedia:

The Dedekind psi
function is the
multiplicative function on the positive integers defined by
$$\psi(n)=n \prod_{p \mid n}\left(1+\frac{1}{p}\right),$$
where the product is taken over all primes $p$ dividing $n$. (By
convention, $\psi (1)=1$.)

It starts with $\psi(n)=1, 3, 4, 6, 6, 12, 8, 12, 12, 18,\dots$, which is OEIS entry A001615.

The wikipedia article references:

*

*Leonard Eugene Dickson "History of the Theory Of Numbers", Vol. 1, p. 123, Chelsea Publishing 1952.

*Journal für die reine und angewandte Mathematik, vol. 83, 1877, p. 288. Cf. H. Weber, Elliptische Functionen, 1901, 244-5; ed. 2, 1008 (Algebra III), 234-5
Similarly, the Mathworld article references:

*

*Cox, D. A. Primes of the Form x2+ny2: Fermat, Class Field Theory and Complex Multiplication. New York: Wiley, p. 228, 1997.


*Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 96, 1994.


*Sloane, N. J. A. Sequence A001615/M2315 in "The On-Line Encyclopedia of Integer Sequences."
