Numbers n such that phi(n) = (sum of digits of n)!

1, 1221, 101600, 112112, 121220, 1310022, 1412010, 1600200, 10071100, 10100350, 10311400, 10612000, 10621000, 11002600, 12130300, 100020080, 102202400, 104111300, 110100530, 113321000, 120020600, 1011041031, 1112011005, 2010003600, 2010232200, 2011012410, 2011110024, 2013030012, 2023030020, 2023210200, 2031011400, 2100710010, 2101140300, 2102050020, 2110110240, 2133012000, 16000132000, 100105041101, 102202041011, 102511020101, 103000314011, 111021340001, 232110023000, 233110101020, 240120002300, 2102001113013, 2200014130011, 3102220000005

OFFSET

1

COMMENTS

Numbers n such that G1(n) = G3(G4(n)).

PROGRAMS

Perl

use ntheory qw(:all);

my @values;
foreach my $t (1 .. 13) {
    my $n = factorial($t);
    foreach my $k (inverse_totient($n)) {
        if (vecsum(split(//, $k)) == $t) {
            push @values, $k;
        }
    }
}

foreach my $value (sort { $a <=> $b } @values) {
    print($value, ", ");
}

Sidef

var values = []

for t in (1..13) {
    var n = t!
    values += n.inverse_totient.grep { .sumdigits == t }
}

say values.sort.join(", ")