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

1,2

Comments

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

Links

Table of n, a(n) for n=1..42.

Formula

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

Prog

(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

Crossrefs

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

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

Sequence in context: A074795 A069577 A282426 * A357186 A316844 A331245

Adjacent sequences: A318778 A318779 A318780 * A318782 A318783 A318784

Keyword

nonn,more

Author

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

Extensions

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

Status

approved