A361419 Numbers k such that there is a unique number m for which the sum of the aliquot infinitary divisors of m (A126168) is k.

0, 6, 7, 9, 11, 18, 32, 44, 56, 62, 72, 82, 94, 96, 98, 102, 104, 110, 116, 122, 132, 136, 138, 146, 150, 152, 178, 180, 182, 210, 222, 226, 230, 236, 238, 242, 248, 252, 264, 272, 284, 292, 296, 304, 322, 332, 338, 342, 350, 356, 360, 374, 382, 390, 392, 404

Offset: 1

Author

Amiram Eldar, Mar 11 2023

Keywords

• nonn

Comments

Numbers k such that A331973(k) = 1.

Links

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

Crossrefs

Cf. A126168, A324277, A331974, A331973, A361420.

Similar sequences: A057709, A357324.

Programs

Mathematica

f[p_, e_] := Module[{b = IntegerDigits[e, 2]}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; is[1] = 0; is[n_] := Times @@ f @@@ FactorInteger[n] - n;
seq[max_] := Module[{v = Table[0, {max}], i}, Do[i = is[k] + 1; If[i <= max, v[[i]]++], {k, 1, max^2}]; -1 + Position[v, 1] // Flatten];
seq[500]

PARI

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

Formula

a(n) = A126168(A361420(n)).