A273157 Numbers which have nonpositive entries in the difference table of their divisors (complement of A273130).

6, 10, 12, 14, 15, 18, 20, 22, 24, 26, 28, 30, 34, 35, 36, 38, 40, 42, 44, 45, 46, 48, 50, 52, 54, 56, 58, 60, 62, 63, 66, 68, 70, 72, 74, 75, 76, 77, 78, 80, 82, 84, 86, 88, 90, 91, 92, 94, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 112, 114, 116, 117

Offset

1,1

Comments

Primorial numbers (A002110) greater than 2 are in this sequence.

Links

Table of n, a(n) for n=1..62.

Example

30 is in this sequence because the difference table of the divisors of 30 is:
[1, 2, 3, 5, 6, 10, 15, 30]
[1, 1, 2, 1, 4, 5, 15]
[0, 1, -1, 3, 1, 10]
[1, -2, 4, -2, 9]
[-3, 6, -6, 11]
[9, -12, 17]
[-21, 29]
[50]

Prog

(Sage)
def nsf(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 True
    return False
print([n for n in range(1, 100) if nsf(n)])

Crossrefs

Cf. A069059, A187202, A273102, A273103, A273109, A273130 (complement).

Sequence in context: A100658 A182301 A069059 * A139587 A201463 A119313

Adjacent sequences: A273154 A273155 A273156 * A273158 A273159 A273160

Keyword

nonn

Author

Peter Luschny, May 16 2016

Status

approved