login
Numbers which have nonpositive entries in the difference table of their divisors (complement of A273130).
1

%I #19 Feb 27 2020 11:51:56

%S 6,10,12,14,15,18,20,22,24,26,28,30,34,35,36,38,40,42,44,45,46,48,50,

%T 52,54,56,58,60,62,63,66,68,70,72,74,75,76,77,78,80,82,84,86,88,90,91,

%U 92,94,96,98,99,100,102,104,105,106,108,110,112,114,116,117

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

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

%e 30 is in this sequence because the difference table of the divisors of 30 is:

%e [1, 2, 3, 5, 6, 10, 15, 30]

%e [1, 1, 2, 1, 4, 5, 15]

%e [0, 1, -1, 3, 1, 10]

%e [1, -2, 4, -2, 9]

%e [-3, 6, -6, 11]

%e [9, -12, 17]

%e [-21, 29]

%e [50]

%o (Sage)

%o def nsf(z):

%o D = divisors(z)

%o T = matrix(ZZ, len(D))

%o for m, d in enumerate(D):

%o T[0, m] = d

%o for k in range(m-1, -1, -1) :

%o T[m-k, k] = T[m-k-1, k+1] - T[m-k-1, k]

%o if T[m-k, k] <= 0: return True

%o return False

%o print([n for n in range(1, 100) if nsf(n)])

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

%K nonn

%O 1,1

%A _Peter Luschny_, May 16 2016