

A333457


a(n) is the smallest number with exactly n divisors that are Moran numbers, or 1 if no such number exists.


0



18, 42, 84, 126, 252, 756, 1998, 1596, 2394, 4662, 4788, 9324, 18648, 23940, 46620, 93240, 139860, 177156, 559440, 354312, 708624, 1062936, 885780, 4606056, 1771560, 3543120, 5314680, 10629360, 38974320, 23030280, 46060560, 69090840, 138181680, 506666160
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OFFSET

1,1


COMMENTS

m is a Moran number if (m / sum of digits of m) is prime (A001101).
Conjecture: For every n there is at least one number k with n divisors Moran numbers.
Conjecture: The terms are divisible by 6.
a(1) = 18, a(2) = 42 and a(3) = 84 are Moran numbers. Not all terms in the sequence are Moran numbers. For example: a(4) = 126 has digsum(126) = 9 and 126 / 9 = 14. Also, the terms a(5)  a(34) are not Moran numbers.


LINKS



EXAMPLE

Of the divisors of 18 (1, 2, 3, 6, 9, 18), only 18 is a Moran number: 18 / digsum (18) = 2.
Of the divisors of 84 (1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84), only 21, 42 and 84 are Moran numbers: 21 / digsum (21) = 7, 42 / digsum (42) = 7 and 84 / digsum (84) = 7.


MATHEMATICA

numDiv[n_] := DivisorSum[n, 1 &, PrimeQ[#/Plus @@ IntegerDigits[#]] &]; a[n_] := Module[{k = 1}, While[numDiv[k] != n, k++]; k]; Array[a, 20] (* Amiram Eldar, May 11 2020 *)


PROG

(Magma) a:=[]; for n in [1..20] do m:=1; while #[d:d in Divisors(m)d mod &+Intseq(d) eq 0 and IsPrime(d div &+Intseq(d))] ne n do m:=m+1; end while; Append(~a, m); end for; a;


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



