A045885 Largest number m such that in base n, the sum of digits in the divisors of m is m (written in base 10).

6, 6, 4, 9, 16, 30, 28, 10, 15, 14, 36, 1, 27, 30, 16, 120, 1, 42, 1, 34, 64, 54, 88, 240, 1, 66, 1, 140, 1, 360, 32, 58, 45, 112, 1, 240, 1, 102, 234, 280, 63, 114, 50, 420, 1, 86, 1, 216, 176, 270, 1, 1, 1, 198, 1, 672, 264, 68, 1, 840, 1, 174, 64, 122, 117

Offset

2,1

Links

Table of n, a(n) for n=2..66.

Example

[ Decimal ] divisors of 15 are (1,3,5,15), 1+3+5+1+5=15.

Prog

(Sage)
def a(n) :
    res = 1
    m = 2
    # A crude bound
    while (n-1)*(m.exact_log(n) + 2) * (2 * (isqrt(m)+1)) >= m :
        if sum(sum(d.digits(n)) for d in divisors(m)) == m :
            res = m
        m += 1
    return res
# Eric M. Schmidt, Jun 27 2015

Crossrefs

Cf. A045884.

Sequence in context: A360828 A209938 A165953 * A019118 A019126 A019206

Adjacent sequences: A045882 A045883 A045884 * A045886 A045887 A045888

Keyword

easy,nonn,base

Author

Author's name lost.

Extensions

Definition corrected by and more terms from Eric M. Schmidt, Jun 27 2015

Status

approved