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

Author

Ilya Gutkovskiy, Dec 03 2022

Keywords

• nonn
• more

Comments

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

Examples

			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.
		

Links

• Eric Weisstein's World of Mathematics, Pyramidal Number
• Index entries for sequences related to divisors of numbers

Crossrefs

Cf. A005179, A358540, A358859, A358861.

Programs

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

Extensions

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