A134194 a(n) = the smallest positive divisor of n that does not occur among the exponents in the prime factorization of n.

1, 2, 3, 1, 5, 2, 7, 1, 1, 2, 11, 3, 13, 2, 3, 1, 17, 3, 19, 4, 3, 2, 23, 2, 1, 2, 1, 4, 29, 2, 31, 1, 3, 2, 5, 1, 37, 2, 3, 2, 41, 2, 43, 4, 3, 2, 47, 2, 1, 5, 3, 4, 53, 2, 5, 2, 3, 2, 59, 3, 61, 2, 3, 1, 5, 2, 67, 4, 3, 2, 71, 1, 73, 2, 3, 4, 7, 2, 79, 2, 1, 2, 83, 3, 5, 2, 3, 2, 89, 3, 7, 4, 3, 2, 5, 2

Offset

1,2

Comments

If n is in A008578, a(n) = n. - Indranil Ghosh, May 16 2017

Links

Indranil Ghosh, Table of n, a(n) for n = 1..10000

Example

The prime factorization of 24 is 2^3 * 3^1. The exponents are 3 and 1. The positive divisors of 24 are 1,2,3,4,6,8,12,24. Therefore since only the divisors 1 and 3 occur among the exponents in the prime factorization of 24, then a(24) = 2 is the smallest divisor not occurring among those exponents.
The prime factorization of 40 is 2^3 * 5^1. The exponents are 3 and 1. The positive divisors of 40 are 1,2,4,5,8,10,20,40. Therefore since only the divisor 1 occurs among the exponents in the prime factorization of 40, then a(40) = 2 is the smallest divisor not occurring among those exponents.

Mathematica

Table[Min[Complement[Divisors[n], Table[FactorInteger[n][[i, 2]], {i, 1, Length[FactorInteger[n]]}]]], {n, 1, 80}] (* Stefan Steinerberger, Aug 30 2008 *)

Prog

(Python)
from sympy import divisors, factorint
def a(n):
    f=factorint(n)
    l=[f[i] for i in f]
    return min(i for i in divisors(n) if i not in l)
print([a(n) for n in range(1, 97)]) # Indranil Ghosh, May 16 2017

Crossrefs

Sequence in context: A353274 A326691 A277698 * A308707 A158584 A086112

Adjacent sequences: A134191 A134192 A134193 * A134195 A134196 A134197

Keyword

nonn

Author

Leroy Quet, Jan 13 2008

Extensions

Corrected and extended by Stefan Steinerberger, Aug 30 2008

Status

approved