i was tring to solve this problem So i`ve to calculate the minimum value of

N so that phi(n)=k

here what i was thinking in :

we could rewrite "k" such that

k=((a-1)*a^x)*((b-1)*b^y) ...... and so on where a,b are primes and x,y some values i`ve to find

then i`ve calculated all the primes where k%(p-1)==0 sorted in increasing order

then for each prime (p) brute force to get the power "a" such that "a" is the maximum value satisfy this relation

k%((p-1)*p^a)==0

then get the new k

k=k/((p-1)*p^a)

then Do the same using the next prime till the k reach 1

after reconstruct N using the primes and it`s values

but this solution dose not work . May some one help in how i could calculate the inverse eular ?!