A273199 Integers which have a positive but not monotone difference table of their divisors.

51, 55, 57, 69, 87, 93, 111, 119, 123, 129, 141, 159, 177, 183, 201, 207, 213, 219, 237, 249, 253, 267, 275, 291, 303, 309, 319, 321, 327, 333, 339, 369, 377, 381, 393, 403, 411, 417, 447, 453, 471, 489, 501, 519, 537, 543, 573, 579, 591, 597

Offset

1,1

Comments

For an integer n>0 and not the unity we define DTD(n) to be the difference table of the divisors of n. We say that DTD(n) is positive if all entries in the table are positive and we call DTD(n) monotone if all rows and all columns of the table are nondecreasing (reading from left to right and from top to bottom).

Links

Table of n, a(n) for n=1..50.

Example

159 is in this sequence because the DTD of 159 has only positive entries but not all columns are nondecreasing:
[  1   3   53 159]
[  2  50  106]
[ 48  56]
[  8]

Prog

(Sage)
def is_A273199(n):
    D = divisors(n)
    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
    non_decreasing = lambda L: all(x<=y for x, y in zip(L, L[1:]))
    b = True
    for k in range(0, len(D)-1):
        b &= non_decreasing(T.row(k)[:len(D)-k])
        b &= non_decreasing(T.column(k)[:len(D)-k])
        if not b: return True
    return False
print([n for n in range(1, 600) if is_A273199(n)])

Crossrefs

Cf. A000040, A246655, A273102, A273130, A273200, A273201.

Sequence in context: A042299 A321962 A060033 * A095525 A045805 A031410

Adjacent sequences: A273196 A273197 A273198 * A273200 A273201 A273202

Keyword

nonn

Author

Peter Luschny, May 17 2016

Status

approved