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A254001 a(n) is the least natural number k such that n^k is abundant or perfect, or a(n) is 0 if all n^k are deficient numbers. 1
0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 2, 0, 0, 0, 1, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 1, 0, 0, 0, 4, 0, 1, 0, 4, 0, 1, 0, 1, 0, 2, 0, 4, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 0, 4, 0, 1, 0, 4, 0, 0, 0, 1, 0, 2, 0, 1, 0, 1, 0, 5, 0, 2, 0, 1, 0, 1, 0, 5, 0, 1, 0, 5, 0, 1, 0, 1, 0, 2, 0, 5, 0, 1, 0, 2, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

COMMENTS

Let p_1, p_2, ..., p_m be the distinct primes dividing n. If (p_1/(p_1 - 1))*(p_2/(p_2 - 1))*...*(p_m/(p_m - 1)) > 2, then sufficiently high powers of n are abundant. Otherwise all powers of n are deficient, and we set a(n)=0.

The sequence is unbounded. In particular, for each N, we have a(A063765(N)) = N.

LINKS

Jeppe Stig Nielsen, Table of n, a(n) for n = 1..10000

EXAMPLE

a(38)=4 because 38^4 is abundant (A023196) while 38^3, 38^2, and 38 are all deficient (A005100).

PROG

(PARI) a(n) = {

primeVect = factor(n)[, 1];

if(prod(i=1, #primeVect, 1-1/primeVect[i])>=1/2, return(0));

for(k=1, 10^99, t=n^k; if(sigma(t)>=2*t, return(k))); }

CROSSREFS

Sequence in context: A108069 A227837 A263099 * A089734 A321375 A307831

Adjacent sequences:  A253998 A253999 A254000 * A254002 A254003 A254004

KEYWORD

nonn,easy

AUTHOR

Jeppe Stig Nielsen, Jan 22 2015

STATUS

approved

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Last modified May 19 10:36 EDT 2019. Contains 323390 sequences. (Running on oeis4.)