A389208 Numbers satisfying Euler's condition for odd perfect numbers, with the squarefree part subtracted: a(n) = A326128(A228058(n)), where A326128(n) = n - A007913(n).

40, 104, 136, 240, 232, 312, 296, 328, 400, 408, 424, 488, 600, 624, 584, 696, 712, 816, 840, 776, 808, 888, 872, 904, 984, 1040, 1096, 1272, 1192, 1360, 1256, 1392, 1440, 1464, 1384, 1560, 1448, 1544, 1576, 1800, 1776, 1752, 1968, 2040, 1832, 1864, 1928, 2200, 2136, 2056, 2320, 2152, 2328, 2216, 2424, 2248, 2544

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..20410

Formula

a(n) = A228058(n) - A389165(n).

a(n) = A389206(n) - A325377(n).

a(n) = A325379(n) + A389207(n).

Prog

(PARI)
up_to = 20410;
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];
A326128(n) = (n-core(n));
A389208(n) = A326128(A228058(n));

Crossrefs

Cf. A228058, A325379, A326128, A388279, A389161, A389165, A389206, A389207, A389209.

Sequence in context: A033832 A235017 A052476 * A043219 A039396 A043999

Adjacent sequences: A389205 A389206 A389207 * A389209 A389210 A389211

Keyword

nonn

Author

Antti Karttunen, Sep 29 2025

Status

approved