A387404 Numbers of the form 12*k + 1 that satisfy Euler's condition for odd perfect numbers (A228058).

325, 637, 925, 1525, 1573, 1813, 1825, 2425, 2725, 2989, 3577, 3757, 3925, 4477, 4525, 4693, 4753, 4825, 5341, 5725, 6025, 6253, 6877, 6925, 7381, 7693, 7825, 8125, 8425, 8725, 8833, 8869, 9325, 9457, 9925, 10225, 10309, 10525, 10693, 10825, 10933, 11221, 11425, 11737, 11809, 12337, 12493, 13189, 13357, 13525, 13573

Offset: 1

Author

Antti Karttunen, Aug 29 2025

Keywords

• nonn
• new

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A017533 and A228058.

Programs

Mathematica

nn = 51; 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&&Mod[n,12]==1, AppendTo[t, n]]]; t (* James C. McMahon, Aug 29 2025 *)

PARI

is_A387404(n) = if(1!=(n%12) || (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));