A280295 - OEIS

A280295

Smallest number with middle divisors whose distance to the next number with middle divisors is n.

1, 2, 9, 20, 72, 144, 425, 532, 651, 1334, 2668, 2928, 6512, 6916, 8400, 8858, 10011, 25350, 28576, 27280, 87053, 113050, 163024, 158952, 132210, 122850, 449123, 178568, 1187394, 185505, 2381025, 1640128, 599205, 1308162, 4180215, 5582876, 2527263, 2577650

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

The original name was: Smallest number with precipice n. Descending by the main diagonal of the pyramid described in A245092, the height difference between the level a(n) (starting from the top) and the level of the next terrace is equal to n.

The structure of the stepped pyramid arises after the 90-degree-zig-zag folding of the diagram of the isosceles triangle A237593.

The terraces at the k-th level of the pyramid are also the parts of the symmetric representation of sigma(k), k >= 1.

The stepped pyramid is also one of the 3D-quadrants of the stepped pyramid described in A244050.

For more information about the precipices see A277437 and A280223.

Is this sequence infinite?

LINKS

Table of n, a(n) for n=1..38.

Omar E. Pol, Perspective view of the stepped pyramid (first 16 levels)

FORMULA

a(n) = A071562(A390114(n)). - Omar E. Pol, Oct 25 2025

EXAMPLE

a(3) = 9 because descending by the main diagonal of the pyramid, the height difference between the level 9 and the level of the next terrace is equal to 3, and 9 is the smallest number with this property.

CROSSREFS

Row 1 of A277437.

Cf. A000203, A196020, A235791, A236104, A237591, A237593, A240542, A244050, A245092, A259179, A262626, A276112, A277437, A279286, A279385, A280223.

Cf. A067742, A071562, A280919, A281012, A390114.

Sequence in context: A259035 A093835 A264294 * A041007 A002360 A100516

Adjacent sequences: A280292 A280293 A280294 * A280296 A280297 A280298

KEYWORD

nonn

AUTHOR

Omar E. Pol, Dec 31 2016

EXTENSIONS

a(6) from Omar E. Pol, Jan 02 2017

a(7)-a(19) and new name from Omar E. Pol, Oct 25 2025

More terms from Sean A. Irvine, Oct 29 2025

STATUS

approved