A318781 A188999(m)/m for the integers m such that A188999(m) is divisible by m, where A188999 is the bi-unitary sigma function.

1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 4, 3, 4, 3, 3, 4, 4, 3, 3, 3, 4, 4, 4, 3, 3, 4, 3, 4, 4, 3, 4, 3, 3, 4, 4, 4, 4, 3

Offset: 1

Author

Michel Marcus, Sep 03 2018, following a suggestion from Felix Fröhlich

Keywords

• nonn
• more

Comments

10496266260480 is a term of A189000 and it is the smallest known value x such that A188999(x)/x is 5.

Crossrefs

Cf. A188999 (bi-unitary sigma), A189000 (multiply perfect for bi-unitary sigma).

Cf. A054030 (analog for sigma), A007691 (multiply perfect for sigma).

Programs

PARI

a188999(n) = my(f = factor(n)); for (i=1, #f~, p = f[i, 1]; e = f[i, 2]; f[i, 1] = if (e % 2, (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1) -p^(e/2)); f[i, 2] = 1; ); factorback(f) \\ after Michel Marcus in A189000
is_a189000(n) = ! frac(a188999(n)/n) \\ after Michel Marcus in A189000
for(n=1, oo, if(is_a189000(n), print1(a188999(n)/n, ", "))) \\ Felix Fröhlich, Sep 03 2018

Formula

a(n) = A188999(A189000(n))/A189000(n).

Extensions

a(33)-a(42) from Giovanni Resta, Sep 03 2018