A389096 a(n) = A162296(A228058(n)), where A162296 is the sum of divisors that have a square factor, and A228058 lists numbers satisfying Euler's condition for odd perfect numbers.

54, 126, 162, 294, 270, 350, 342, 378, 702, 450, 486, 558, 726, 686, 666, 750, 810, 882, 1014, 882, 918, 950, 990, 1026, 1050, 1638, 1242, 1350, 1350, 2106, 1422, 1470, 1734, 1550, 1566, 1694, 1638, 1746, 1782, 2166, 1862, 1850, 2058, 2178, 2070, 2106, 2178, 4254, 2250, 2322, 3510, 2430, 2450, 2502, 2550, 2538

Offset

1,1

Links

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

Formula

a(n) = A389203(n) - A389164(n).

a(n) = A325320(n) + A228058(n).

a(n) = A325378(n) + A389164(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];
A162296(n) = sumdiv(n, d, d*(1-issquarefree(d)));
A389096(n) = A162296(A228058(n));

Crossrefs

Cf. A162296, A228058, A325320, A325378, A389164, A389203.

Sequence in context: A043446 A044241 A044622 * A255021 A184067 A044305

Adjacent sequences: A389093 A389094 A389095 * A389097 A389098 A389099

Keyword

nonn

Author

Antti Karttunen, Sep 29 2025

Status

approved