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A254571 Least multiplier k such that k*n is abundant or perfect (A023196). 2
6, 3, 2, 3, 4, 1, 4, 3, 2, 2, 6, 1, 6, 2, 2, 3, 6, 1, 6, 1, 2, 3, 6, 1, 4, 3, 2, 1, 6, 1, 6, 3, 2, 3, 2, 1, 6, 3, 2, 1, 6, 1, 6, 2, 2, 3, 6, 1, 4, 2, 2, 2, 6, 1, 4, 1, 2, 3, 6, 1, 6, 3, 2, 3, 4, 1, 6, 3, 2, 1, 6, 1, 6, 3, 2, 3, 4, 1, 6, 1, 2, 3, 6, 1, 4, 3, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A254572(n)=a(n)*n for the actual non-deficient numbers.

The range is {1,2,3,4,6}. Clearly a(n) <= 6 because 6*n is abundant for any n. No n can have a(n)=5. Suppose otherwise. There exists a prime p smaller than 5 which does not divide n (if not, 6|n and a(n)=1). That prime p (either 2 or 3) will boost the abundancy more than does 5. In particular (sigma(p*n))/(p*n) > (sigma(5*n))/(5*n) >= 2, but then a(n) should be p, a contradiction.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(A023196(n)) = 1. - Michel Marcus, Feb 02 2015

MAPLE

f:= proc(n) local k; uses numtheory;

      for k from 1 to 4 do if sigma(k*n)>=2*k*n then return k fi od:

      6

end proc:

map(f, [$1..100]); # Robert Israel, Feb 10 2019

PROG

(PARI) a(n) = for(k=1, 6, if(sigma(k*n)>=2*k*n, return(k)))

CROSSREFS

Cf. A023196, A254572.

Sequence in context: A068996 A068924 A106224 * A244815 A226579 A129203

Adjacent sequences:  A254568 A254569 A254570 * A254572 A254573 A254574

KEYWORD

nonn,easy

AUTHOR

Jeppe Stig Nielsen, Feb 01 2015

STATUS

approved

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Last modified November 17 23:26 EST 2019. Contains 329242 sequences. (Running on oeis4.)