A389198 Sum of unitary divisors of the numbers satisfying Euler's condition for odd perfect numbers: a(n) = A034448(A228058(n)).

60, 140, 180, 300, 300, 364, 380, 420, 492, 468, 540, 620, 732, 700, 740, 780, 900, 900, 1020, 980, 1020, 988, 1100, 1140, 1092, 1148, 1380, 1404, 1500, 1476, 1580, 1500, 1740, 1612, 1740, 1708, 1820, 1940, 1980, 2172, 1900, 1924, 2100, 2196, 2300, 2340, 2420, 3000, 2340, 2580, 2460, 2700, 2548, 2780, 2652, 2820

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..27274

Formula

a(n) = A228058(n) + A325823(n).

a(n) = A325377(n) + A325824(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];
A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); };
A389198(n) = A034448(A228058(n));

Crossrefs

Cf. A034448, A228058, A325377, A325823, A325824.

Sequence in context: A181190 A246474 A334407 * A385054 A336628 A336443

Adjacent sequences: A389195 A389196 A389197 * A389199 A389200 A389201

Keyword

nonn

Author

Antti Karttunen, Sep 29 2025

Status

approved