login
A140864
Smallest odd number with same number of divisors as 3*a(n-1).
2
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
1,2
LINKS
Dimitri Papadopoulos, Table of n, a(n) for n = 1..56
EXAMPLE
9*3=27 has 4 divisors, but smallest odd number with 4 divisors is 15.
PROG
(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
CROSSREFS
Cf. A053624, A019505. d(a(n)) = A036451(n) for first 18 terms.
Sequence in context: A053624 A348198 A119239 * A171929 A188597 A330815
KEYWORD
nonn
AUTHOR
J. Lowell, Jul 20 2008
EXTENSIONS
a(10) through a(28) from Klaus Brockhaus, Jul 23 2008
a(29) through a(56) from Dimitri Papadopoulos, May 08 2019
STATUS
approved