A273130 Numbers which have only positive entries in the difference table of their divisors.
1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 33, 37, 39, 41, 43, 47, 49, 51, 53, 55, 57, 59, 61, 64, 65, 67, 69, 71, 73, 79, 81, 83, 85, 87, 89, 93, 95, 97, 101, 103, 107, 109, 111, 113, 115, 119, 121, 123, 125, 127, 128, 129, 131, 133
Offset: 1
Keywords
Examples
85 is in the sequence because the difference table of the divisors of 85 has only entries greater than 0: [1, 5, 17, 85] [4, 12, 68] [8, 56] [48]
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
Select[Range@ 1000, {} == NestWhile[ Differences, Divisors @ #, # != {} && Min[#] > 0 &] &] (* Giovanni Resta, May 16 2016 *) -
PARI
has(v)=if(#v<2, v[1]>0, if(vecmin(v)<1, 0, has(vector(#v-1,i,v[i+1]-v[i])))) is(n)=has(divisors(n)) \\ Charles R Greathouse IV, May 16 2016
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Sage
def sf(z): D = divisors(z) T = matrix(ZZ, len(D)) for m, d in enumerate(D): T[0, m] = d for k in range(m-1, -1, -1) : T[m-k, k] = T[m-k-1, k+1] - T[m-k-1, k] if T[m-k, k] <= 0: return False return True print([z for z in range(1,100) if sf(z)])
Comments