A140864 Smallest odd number with same number of divisors as 3*a(n-1).
1, 3, 9, 15, 45, 105, 315, 945, 2835, 3465, 10395, 31185, 45045, 135135, 405405, 675675, 2027025, 3828825, 11486475, 34459425, 72747675, 218243025, 654729075, 1527701175, 4583103525, 11712375675, 35137127025, 105411381075
Offset: 1
Keywords
Examples
9*3=27 has 4 divisors, but smallest odd number with 4 divisors is 15.
Links
- Dimitri Papadopoulos, Table of n, a(n) for n = 1..56
Programs
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PARI
a(nn) = {ia = 1; print1(ia, ", "); for (n = 1, nn - 1, nd = numdiv(3*ia); forstep(i = 1, 3*ia, 2, if (numdiv(i) == nd, ia = i; break;);); print1(ia, ", "););} \\ Michel Marcus, Jun 14 2013 -
PARI
{/*prints b-file for A140864 - add more for loops for more terms*/ print("#A140864"); print(1" "1); print(2" "3); n = 3; for(p=3,56,tau = numdiv(3*n); exp3n=factor(n)[1,2];delta = bigomega(exp3n+2) - bigomega(exp3n+1); delta = max(delta+1,2); var = exp3n+delta; num = 10^1000; for( n1=1, var, for (n2=0, n1, for( n3=0, n2, for( n4=0, n3, for( n5=0, n4, for( n6=0, n5, for( n7=0, n6, for( n8=0, n7, for( n9=0, n8, for( n10=0, n9, for( n11=0, n10, for( n12=0, n11, for( n13=0, n12, for( n14=0, n13, for( n15=0, n14, if( (n1+1) * (n2+1) * (n3+1) * (n4+1) * (n5+1) * (n6+1) * (n7+1) * (n8+1) * (n9+1) * (n10+1) * (n11+1) * (n12+1) * (n13+1) * (n14+1) * (n15+1) == tau, numtemp = prime(2)^n1 * prime(3)^n2 * prime(4)^n3 * prime(5)^n4 * prime(6)^n5 * prime(7)^n6 * prime(8)^n7 * prime(9)^n8 * prime(10)^n9 * prime(11)^n10 * prime(12)^n11 * prime(13)^n12 * prime(14)^n13 * prime(15)^n14 * prime(16)^n15; if(numtemp < num, num = numtemp); ));););););););) ;);););) ;););); print(p" "num); n=num;)} \\ Dimitri Papadopoulos, May 08 2019
Extensions
a(10) through a(28) from Klaus Brockhaus, Jul 23 2008
a(29) through a(56) from Dimitri Papadopoulos, May 08 2019