

A324458


Numbers m > 1 such that every prime divisor p of m satisfies s_p(m) = p.


6



45, 325, 405, 637, 891, 1729, 2821, 3751, 4961, 6517, 7381, 8125, 8281, 10625, 13357, 21141, 26353, 28033, 29341, 31213, 33125, 35443, 46657, 47081, 58621, 65341, 74431, 78625, 81289, 94501, 98125, 99937, 123823, 146461, 231601, 236321, 252601, 254221, 294409
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OFFSET

1,1


COMMENTS

The function s_p(m) gives the sum of the basep digits of m.
The sequence contains the primary Carmichael numbers A324316.
Being a subsequence of A324460, a term m has the following properties:
m must have at least 2 prime factors. If m = p1^e1 * p2^e2 with two primes p1 and p2, then e1 + e2 >= 3.
Each prime factor p of m satisfies the inequalities p < m^(1/(ord_p(m)+1)) <= sqrt(m), where ord_p(m) gives the maximum exponent e such that p^e divides m.
In the terminology of A324460, the prime factorization of m equals a strict sdecomposition of m.
See Kellner 2019.


LINKS



EXAMPLE

The number 45 has the prime factors 3 and 5. Since s_3(45) = 3 and s_5(45) = 5, 45 is a member.


MATHEMATICA

s[n_, p_] := If[n < 1  p < 2, 0, Plus @@ IntegerDigits[n, p]];
f[n_] := AllTrue[Transpose[FactorInteger[n]][[1]], s[n, #] == # &];
Select[Range[10^7], f[#] &]


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



