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 A119357 Values of n such that the number of distinct nonzero sums of distinct divisors of n is less than 2^tau(n) - 1 (clearly, the latter is the largest number of possible distinct sums, tau(n) being the number of divisors of n (A000005)). Equivalently: values of n for which there exist two distinct subsets of the set of divisors of n, having the same sum. 1
 6, 12, 18, 20, 24, 28, 30, 36, 40, 42, 45, 48, 54, 56, 60, 63, 66, 70, 72, 78, 80, 84, 88, 90, 96, 99, 100, 102, 104, 105, 108, 110, 112, 114, 117, 120, 126, 130, 132, 135, 138, 140, 144, 150, 154, 156, 160, 162, 165, 168, 170, 174, 176, 180, 182, 186, 189, 192, 195 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sequence is closed with respect to multiplication by positive integers (i.e. any multiple of any term in the sequence is in the sequence). The primitive entries of the sequence, i.e. those that are not multiples of other terms of the sequence, are given in A119425 (the first five are 6,20,28,45 and 63). The number of distinct sums of distinct divisors of n are given in A119347 and the actual sums are given in row n of the triangle A119348. Subsequence of A051774 (Max Alekseyev) LINKS EXAMPLE 6 is in the sequence because from the divisors of 6, namely 1,2,3,6, we can form by addition 12 sums (1,2,3,...,12) and 12 < 2^tau(6)-1=2^4-1=15. Sequence contains, for example, all multiples of 6 (1+2=3), all multiples of 20 (1+4=5), all multiples of 28 (1+2+4=7), all multiples of 63 (1+9=3+7). MAPLE with(numtheory): with(linalg): s:=proc(n) local dl, t:dl:=convert(divisors(n), list): t:=tau(n): nops({seq(innerprod(dl, convert(2^t+i, base, 2)[1..t]), i=1..2^t-1)}) end: a:=proc(n) if s(n)<2^tau(n)-1 then n else fi end: seq(a(n), n=1..230); CROSSREFS Cf. A000005, A051774, A119347, A119348, A119425. Sequence in context: A328608 A328671 A051774 * A097216 A346695 A326133 Adjacent sequences:  A119354 A119355 A119356 * A119358 A119359 A119360 KEYWORD nonn AUTHOR Emeric Deutsch, May 18 2006 STATUS approved

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Last modified October 26 05:34 EDT 2021. Contains 348256 sequences. (Running on oeis4.)