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
Giovanni Resta, Table of n, a(n) for n = 1..10000
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
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Oct 10 2019
STATUS
approved