A324455 - OEIS

A324455

Numbers m > 1 such that there exists a divisor g > 1 of m which satisfies s_g(m) >= g.

6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 30, 33, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 56, 57, 58, 60, 62, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

The function s_g(m) gives the sum of the base-g digits of m.

The sequence is infinite, since it contains A324460 and the Carmichael numbers A002997.

A term m must have at least 2 prime factors, and the divisor g satisfies the inequalities 1 < g < m^(1/(ord_g(m)+1)) <= sqrt(m), where ord_g(m) gives the maximum exponent e such that g^e divides m.

See Kellner 2019.

LINKS

Bernd C. Kellner, Table of n, a(n) for n = 1..743

Bernd C. Kellner, On primary Carmichael numbers, Integers 22 (2022), Article #A38, 39 pp.; arXiv:1902.11283 [math.NT], 2019.

EXAMPLE

6 is a member, since 2 divides 6 and s_2(6) = 2.

MATHEMATICA

s[n_, g_] := If[n < 1 || g < 2, 0, Plus @@ IntegerDigits[n, g]];

f[n_] := AnyTrue[Divisors[n], s[n, #] >= # &];

Select[Range[1000], f[#] &]

CROSSREFS

Subsequences are A002997, A324315, A324316, A324456, A324457, A324458, A324459, A324460.