A358860 a(n) is the smallest n-gonal pyramidal number divisible by exactly n n-gonal pyramidal numbers.

56, 140, 4200, 331800, 611520, 8385930, 1071856800, 41086892000, 78540000, 38102655397426620, 59089382788800, 22241349900, 2326493030400, 7052419469195100, 886638404171520

Offset

3,1

Comments

The corresponding indices of n-gonal pyramidal numbers are 6, 7, 20, 79, 90, 203, ...

Links

Table of n, a(n) for n=3..17.

Eric Weisstein's World of Mathematics, Pyramidal Number

Index entries for sequences related to divisors of numbers

Example

a(4) = 140, because 140 is a square pyramidal number that has 4 square pyramidal divisors {1, 5, 14, 140} and this is the smallest such number.

Prog

(PARI)
pyramidal(k, r)=(k*(k+1)*((r-2)*k + (5-r)))\6;
ispyramidal(n, r) = pyramidal(sqrtnint(6*n\(r-2) + sqrtnint(n, 3), 3), r) == n;
a(n) = if(n<3, return()); for(k=1, oo, my(t=pyramidal(k, n)); if(sumdiv(t, d, ispyramidal(d, n)) == n, return(t))); \\ Daniel Suteu, Dec 06 2022

Crossrefs

Cf. A005179, A358540, A358859, A358861.

Sequence in context: A241287 A201096 A358540 * A226128 A038850 A220042

Adjacent sequences: A358857 A358858 A358859 * A358861 A358862 A358863

Keyword

nonn,more

Author

Ilya Gutkovskiy, Dec 03 2022

Extensions

a(9)-a(17) from Daniel Suteu, Dec 06 2022

Status

approved