A358512 a(n) is the smallest number k with exactly n divisors that can be written in the form m + digsum(m), for some m (A176995).

1, 2, 4, 8, 12, 30, 24, 80, 48, 72, 96, 192, 120, 180, 288, 612, 240, 624, 420, 360, 480, 900, 1632, 960, 1200, 720, 840, 1560, 2100, 1260, 1440, 3420, 2640, 3024, 1680, 2880, 8316, 4620, 3600, 3780, 4200, 2520, 3360, 6240, 9900, 6300, 7200, 8640, 6720, 13200, 7920

Offset

0,2

Links

David A. Corneth, Table of n, a(n) for n = 0..2499

Example

1 cannot be written in the form m + digsum(m), so a(0) = 1.
2 has divisors 1 and 2, and only 2 is written 2 = 1 + digsum(1), so a(1) = 2.
3 has divisors 1 and 3 that cannot be written in the form m + digsum(m).
4 has divisors 1, 2, 4, but only 2 = 1 + digsum(1) and 4 = 2 + digsum(2), so a(2) = 4.

Prog

(Magma) f:=func<n|exists(c){s:s in [0..n]| n eq s+&+Intseq(s)}>; a:=[]; for n in [0..50] do k:=1; while #[d:d in Divisors(k)|f(d)] ne n do k:=k+1; end while; Append(~a, k); end for; a;
(PARI) is_A003052(n)={for(i=1, min(n\2, 9*#digits(n)), sumdigits(n-i)==i && return); n}
a(n) = my(k=1); while (sumdiv(k, d, !is_A003052(d)) != n, k++); k; \\ Michel Marcus, Dec 13 2022

Crossrefs

Cf. A003052, A062028, A176995, A230093.

Sequence in context: A115386 A306491 A058771 * A036493 A082906 A364768

Adjacent sequences: A358509 A358510 A358511 * A358513 A358514 A358515

Keyword

nonn,base

Author

Marius A. Burtea, Dec 04 2022

Status

approved