A389203 Sum of divisors of the numbers satisfying Euler's condition for odd perfect numbers (A228058).

78, 182, 234, 342, 390, 434, 494, 546, 726, 558, 702, 806, 798, 798, 962, 930, 1170, 1026, 1098, 1274, 1326, 1178, 1430, 1482, 1302, 1694, 1794, 1674, 1950, 2178, 2054, 1710, 1842, 1922, 2262, 1862, 2366, 2522, 2574, 2286, 2166, 2294, 2394, 2394, 2990, 3042, 3146, 4446, 2790, 3354, 3630, 3510, 3038, 3614, 3162

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to sigma(n).

Formula

a(n) = A000203(A228058(n)).

a(n) = A389200(n) * A389201(n).

a(n) = A228058(n) + A325377(n).

Mathematica

nn = 100; n = 1; t = {}; While[Length[t] < nn, n = n + 2; {p, e} = Transpose[FactorInteger[n]]; od = Select[e, OddQ]; If[Length[e] > 1 && Length[od] == 1 && Mod[od[[1]], 4] == 1 && Mod[p[[Position[e, od[[1]]][[1, 1]]]], 4] == 1, AppendTo[t, n]]]; DivisorSigma[1, t] (* James C. McMahon, Sep 30 2025 *)

Prog

(PARI)
up_to = 20000;
isA228058(n) = if(!(n%2)||(omega(n)<2), 0, my(f=factor(n), y=0); for(i=1, #f~, if(1==(f[i, 2]%4), if((1==y)||(1!=(f[i, 1]%4)), return(0), y=1), if(f[i, 2]%2, return(0)))); (y));
A228058list(up_to) = { my(v=vector(up_to), k=0, n=0); while(k<up_to, n++; if(isA228058(n), k++; v[k] = n)); (v); };
v228058 = A228058list(up_to);
A228058(n) = v228058[n];
A389203(n) = sigma(A228058(n));

Crossrefs

Cf. A000203, A228058, A325377, A389200, A389201.

Sequence in context: A119146 A044410 A044791 * A389179 A232386 A257484

Adjacent sequences: A389200 A389201 A389202 * A389204 A389205 A389206

Keyword

nonn

Author

Antti Karttunen, Sep 28 2025

Status

approved