

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
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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. 2130.


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



