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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.
Amin Witno and Khaled Hyasat, Solutions to two open questions on super Niven numbers, Global Journal of Pure and Applied Mathematics, Vol. 6, No. 3 (2010), pp. 227-231, alternative link.
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
Subsequence of A005349.
Sequence in context: A271955 A365420 A342650 * A342262 A255734 A357142
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Oct 10 2019
STATUS
approved

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Last modified June 23 05:53 EDT 2024. Contains 373629 sequences. (Running on oeis4.)