A372743 a(n) is the unique number m such that A336563(m) = A372742(n).

4, 9, 25, 49, 121, 27, 169, 289, 24, 361, 529, 54, 841, 961, 36, 1369, 1681, 1849, 2209, 2809, 343, 3481, 3721, 4489, 5041, 5329, 6241, 100, 6889, 189, 7921, 72, 9409, 112, 10201, 10609, 11449, 11881, 686, 12769, 16129, 17161, 225, 18769, 19321, 196, 22201, 160

Offset: 1

Author

Amiram Eldar, May 12 2024

Keywords

• nonn

Comments

Includes all the squares of primes (A001248).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A336563, A372742.

A001248 is a subsequence.

Similar sequences: A357313, A357325, A361420.

Programs

Mathematica

f[p_, e_] := (p^(e + 1) - 1)/(p - 1) - 1; s[1] = 0; s[n_] := Times @@ f @@@ FactorInteger[n] - n; seq[max_] := Module[{v = w = Table[0, {max}], i}, Do[i = s[k]; If[1 <= i <= max, v[[i]]++; w[[i]] = k], {k, 1, max^2}]; w[[Position[v, 1] // Flatten]]]; seq[200]

PARI

s(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i, 1]^(f[i, 2] + 1) - 1)/(f[i, 1] -1) - 1) - n;}
lista(nmax) = {my(v = w = vector(nmax), i); for(k = 1, nmax^2, i = s(k); if(i > 0 && i <= nmax, v[i]++; w[i] = k)); for(k = 1, nmax, if(v[k] == 1, print1(w[k], ", ")));}

Formula

A336563(a(n)) = A372742(n).