A358543
a(n) is the smallest number with exactly n divisors that are square pyramidal numbers.
Original entry on oeis.org
1, 5, 30, 140, 420, 1540, 4620, 13860, 78540, 157080, 471240, 1141140, 3603600, 3423420, 13693680, 30630600, 58198140, 116396280, 214414200, 428828400, 581981400, 1163962800, 5354228880, 4073869800, 8147739600, 26771144400, 36082846800, 80313433200, 93699005400, 187398010800
Offset: 1
a(3) = 30 because 30 has 3 square pyramidal divisors {1, 5, 30} and this is the smallest such number.
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issqpyr(n) = my(m = sqrtnint(3*n, 3)); n==m*(m+1)*(2*m+1)/6; \\ A253903
a(n) = my(k=1); while (sumdiv(k, d, issqpyr(d)) != n, k++); k; \\ Michel Marcus, Nov 21 2022
A358544
a(n) is the smallest number with exactly n divisors that are centered triangular numbers.
Original entry on oeis.org
1, 4, 20, 320, 460, 5440, 14260, 12920, 168640, 103360, 594320, 3878720, 2377280, 9211960, 18423920, 36847840, 125995840, 73695680, 865924240, 976467760, 1952935520, 3463696960, 3905871040, 31246968320, 22946992360
Offset: 1
a(3) = 20 because 20 has 3 centered triangular divisors {1, 4, 10} and this is the smallest such number.
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isct(n) = my(k=(2*n-2)/3, m); (n==1) || ((denominator(k)==1) && (m=sqrtint(k)) && (m*(m+1)==k)); \\ A005448
a(n) = my(k=1); while (sumdiv(k, d, isct(d)) != n, k++); k; \\ Michel Marcus, Nov 21 2022
A358541
a(n) is the smallest number with exactly n divisors that are centered n-gonal numbers.
Original entry on oeis.org
20, 325, 912, 43771, 234784, 11025, 680680, 9143308361, 2470852896
Offset: 3
a(5) = 912 because 912 has 5 centered pentagonal divisors {1, 6, 16, 76, 456} and this is the smallest such number.
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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