A323173 Sum of divisors computed for conjugated prime factorization: a(n) = A000203(A122111(n)).

1, 3, 7, 4, 15, 12, 31, 6, 13, 28, 63, 18, 127, 60, 39, 8, 255, 24, 511, 42, 91, 124, 1023, 24, 40, 252, 31, 90, 2047, 72, 4095, 12, 195, 508, 120, 32, 8191, 1020, 403, 56, 16383, 168, 32767, 186, 93, 2044, 65535, 36, 121, 78, 819, 378, 131071, 48, 280, 120, 1651, 4092, 262143, 96, 524287, 8188, 217, 14, 600, 360, 1048575, 762, 3315, 234

Offset: 1

Author

Antti Karttunen, Jan 10 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4096
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A038712, A122111, A322819, A323174.

Cf. also A323243.

Programs

Mathematica

A122111[n_] := Product[Prime[Sum[If[j < i, 0, 1], {j, #}]], {i, Max[#]}]&[ Flatten[Table[Table[PrimePi[f[[1]]], {f[[2]]}], {f, FactorInteger[n]}]]];
a[n_] := With[{k = A122111[n]}, DivisorSigma[1, k]];
Array[a, 70] (* Jean-François Alcover, Sep 23 2020 *)

PARI

A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
A323173(n) = sigma(A122111(n));

Formula

a(n) = A000203(A122111(n)).

a(n) = 2*A122111(n) - A323174(n).

a(n) = A322819(n) * A038712(A122111(n)).