|
|
A328273
|
|
Super Niven numbers: numbers divisible by the sums of all the nonempty subsets of their nonzero digits.
|
|
4
|
|
|
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 20, 24, 30, 36, 40, 48, 50, 60, 70, 80, 90, 100, 102, 110, 120, 140, 150, 200, 204, 210, 220, 240, 280, 300, 306, 330, 360, 400, 408, 420, 440, 480, 500, 510, 540, 550, 600, 630, 660, 700, 770, 800, 840, 880, 900, 990, 1000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
This sequence is infinite since if m is in the sequence then 10*m is also in the sequence.
Saadatmanesh et al. proved that:
1) The only odd terms are 1, 3, 5, 7, and 9.
2) If m is a super Niven number with k nonzero digits, then m is divisible by all the numbers 1 <= j <= k.
3) The only terms without the digit zero are 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 24, 36, and 48.
|
|
REFERENCES
|
Majid Saadatmanesh, Super Niven numbers, MS thesis, Central Missouri State University, 1991.
|
|
LINKS
|
Majid Saadatmanesh, Robert E. Kennedy, and Curtis Cooper, Super Niven numbers, Mathematics in College (1992), pp. 21-30.
|
|
EXAMPLE
|
12 is in the sequence since the nonempty subsets of its nonzero digits are {1}, {2}, {1, 2}, whose sums, 1, 2, 3, are all divisors of 12.
|
|
MATHEMATICA
|
superNivenQ[n_] := AllTrue[Union[Total /@ Rest @ Subsets[Select[IntegerDigits[n], # > 0 &]]], Divisible[n, #] &]; Select[Range[1000], superNivenQ]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|