A136641 a(n) is the smallest positive integer that is coprime to n and has n divisors.

1, 3, 4, 15, 16, 175, 64, 105, 100, 567, 1024, 1925, 4096, 3645, 784, 945, 65536, 13475, 262144, 6237, 1600, 295245, 4194304, 25025, 1296, 2657205, 4900, 40095, 268435456, 3776773, 1073741824, 10395, 25600, 215233605, 5184, 175175, 68719476736, 1937102445, 102400

Offset: 1

Author

Leroy Quet, Apr 14 2008

Keywords

• nonn

Comments

Is this the same as the least index m where A090387(m) = n? - Michel Marcus, Mar 25 2022

For p prime, a(p) = 2^(p-1) for p > 2, a(2*p) = 3^(p-1)*5 for p > 5, a(3*p) = 2^(p-1)*25 for p > 3, a(5*p) = 2^(p-1)*3^4 for p >5, ... . - Michael S. Branicky, Mar 26 2022

Examples

			The sequence of positive integers each with 9 divisors starts: 36, 100, 196, 225, 256, ... Now 36 is not coprime to 9. But 100, the next bigger value with 9 divisors, is. So a(9) = 100.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..65

Crossrefs

Cf. A000005, A073904, A090387.

Programs

PARI

a(n) = my(k=1); while ((gcd(n,k) != 1) || (numdiv(k) != n), k++); k; \\ Michel Marcus, Mar 25 2022

Python

from math import gcd
from sympy import divisor_count
def a(n):
    k = 1
    while gcd(n, k) != 1 or divisor_count(k) != n: k += 1
    return k
print([a(n) for n in range(1, 19)]) # Michael S. Branicky, Mar 25 2022

Extensions

a(11)-a(36) from Sean A. Irvine, May 03 2010

a(37) and beyond from Michael S. Branicky, Mar 26 2022