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a(n) is the smallest n-gonal pyramidal number divisible by exactly n n-gonal pyramidal numbers.
3

%I #20 Dec 08 2022 07:36:15

%S 56,140,4200,331800,611520,8385930,1071856800,41086892000,78540000,

%T 38102655397426620,59089382788800,22241349900,2326493030400,

%U 7052419469195100,886638404171520

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

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PyramidalNumber.html">Pyramidal Number</a>

%H <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>

%e 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.

%o (PARI)

%o pyramidal(k,r)=(k*(k+1)*((r-2)*k + (5-r)))\6;

%o ispyramidal(n, r) = pyramidal(sqrtnint(6*n\(r-2) + sqrtnint(n, 3), 3), r) == n;

%o 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

%Y Cf. A005179, A358540, A358859, A358861.

%K nonn,more

%O 3,1

%A _Ilya Gutkovskiy_, Dec 03 2022

%E a(9)-a(17) from _Daniel Suteu_, Dec 06 2022