A358859
a(n) is the smallest n-gonal number divisible by exactly n n-gonal numbers.
Original entry on oeis.org
6, 36, 210, 4560, 6426, 326040, 4232250, 1969110, 296676380, 4798080, 166289760, 73765692000, 712750500, 50561280, 33944067893736, 2139168754800, 4292572951800, 1414764341760, 72461756727360, 180975331456920, 1870768457500800, 5498331930000, 153698278734000
Offset: 3
a(5) = 210, because 210 is a pentagonal number that has 5 pentagonal divisors {1, 5, 35, 70, 210} and this is the smallest such number.
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a(n) = if(n<3, return()); for(k=1, oo, my(t=(k*(n*k - n - 2*k + 4))\2); if(sumdiv(t, d, ispolygonal(d, n)) == n, return(t))); \\ Daniel Suteu, Dec 04 2022
A358860
a(n) is the smallest n-gonal pyramidal number divisible by exactly n n-gonal pyramidal numbers.
Original entry on oeis.org
56, 140, 4200, 331800, 611520, 8385930, 1071856800, 41086892000, 78540000, 38102655397426620, 59089382788800, 22241349900, 2326493030400, 7052419469195100, 886638404171520
Offset: 3
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.
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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
A359231
a(n) is the smallest centered triangular number divisible by exactly n centered triangular numbers.
Original entry on oeis.org
1, 4, 64, 5860, 460, 74260, 14260, 1221760, 5567104, 103360, 20120860, 169096960, 1211757760, 31286787760, 31498960, 114183284260, 1553569960, 33186496960, 446613160960, 43581101074960, 274644405760, 64262632960, 121634429663260, 5786547945760
Offset: 1
a(5) = 460, because 460 is a centered triangular number that has 5 centered triangular divisors {1, 4, 10, 46, 460} and this is the smallest such number.
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// Note: the program below finds all terms through a(22) except for
// a(20) = 43581101074960, which would be reached at k = 5390183.
a := [ 0 : n in [ 1 .. 22 ] ];
for k in [ 0 .. 550000 ] do
c := 3*((k*(k - 1)) div 2) + 1;
D := Divisors(c);
n := 0;
for d in D do
if d mod 3 eq 1 then
if IsSquare(((d - 1) div 3)*8 + 1) then
n +:= 1;
end if;
end if;
end for;
if a[n] eq 0 then
a[n] := c;
end if;
end for;
a; // Jon E. Schoenfield, Dec 25 2022
A359232
a(n) is the smallest centered square number divisible by exactly n centered square numbers.
Original entry on oeis.org
1, 5, 25, 925, 1625, 1105, 47125, 350285, 493025, 3572465, 47074105, 13818025, 4109345825, 171921425, 294346585, 130334225125, 190608050165, 2687125303525, 2406144489125, 5821530534625, 49723952067725, 1500939251825, 665571884367325, 8362509238504525, 1344402738869125
Offset: 1
a(5) = 1625, because 1625 is a centered square number that has 5 centered square divisors {1, 5, 13, 25, 1625} and this is the smallest such number.
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a := [ 0 : n in [ 1 .. 17 ] ];
for k in [ 0 .. 310000 ] do
c := 2*k*(k+1)+1;
D := Divisors(c);
n := 0;
for d in D do
if IsSquare(2*d - 1) then
n +:= 1;
end if;
end for;
if a[n] eq 0 then
a[n] := c;
end if;
end for;
a; // Jon E. Schoenfield, Dec 24 2022
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a(n) = for(k=0, oo, my(t=2*k*(k+1)+1); if(sumdiv(t, d, issquare(2*d-1)) == n, return(t))); \\ Daniel Suteu, Dec 31 2022
Showing 1-4 of 4 results.
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