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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 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 Subsequence of A005349. Sequence in context: A271955 A365420 A342650 * A342262 A255734 A357142 Adjacent sequences: A328270 A328271 A328272 * A328274 A328275 A328276 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.)