A389207 Sum of all other proper divisors except the squarefree part applied to the numbers satisfying Euler's condition for odd perfect numbers: a(n) = A326127(A228058(n)).

28, 52, 64, 92, 100, 96, 124, 136, 316, 116, 172, 196, 188, 148, 232, 176, 280, 176, 248, 304, 316, 216, 340, 352, 236, 628, 424, 296, 460, 784, 484, 260, 392, 336, 532, 276, 556, 592, 604, 476, 316, 396, 344, 320, 700, 712, 736, 2236, 476, 784, 1252, 820, 516, 844, 536, 856, 428, 892, 668, 576, 952, 596, 964, 404

Offset

1,1

Links

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

Formula

a(n) = A389206(n) - A228058(n).

a(n) = A325377(n) - A389165(n).

a(n) = A389208(n) - A325379(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];
A326127(n) = (sigma(n)-core(n)-n);
A389207(n) = A326127(A228058(n));

Crossrefs

Cf. A228058, A325377, A325379, A326127, A388279, A389161, A389165, A389206, A389208, A389209.

Sequence in context: A063770 A161923 A309145 * A039772 A291855 A181792

Adjacent sequences: A389204 A389205 A389206 * A389208 A389209 A389210

Keyword

nonn

Author

Antti Karttunen, Sep 29 2025

Status

approved