

A215926


Smallest deficient number k such that the product k*n is nondeficient (perfect or abundant).


1



3, 2, 3, 4, 1, 4, 3, 2, 2, 8, 1, 8, 2, 2, 3, 16, 1, 16, 1, 2, 3, 16, 1, 4, 3, 2, 1, 16, 1, 16, 3, 2, 3, 2, 1, 32, 3, 2, 1, 32, 1, 32, 2, 2, 3, 32, 1, 4, 2, 2, 2, 32, 1, 4, 1, 2, 3, 32, 1, 32, 3, 2, 3, 4, 1, 64, 3, 2, 1, 64, 1, 64, 3, 2, 3, 4, 1, 64, 1, 2, 3
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OFFSET

2,1


COMMENTS

If n is perfect or abundant then a(n) = 1.
Conjecture: a(n) is 1, 3, or a power of 2.
Conjecture: The first occurrence of 2^m happens at A014210(m).


LINKS

Michel Marcus, Table of n, a(n) for n = 2..1000


EXAMPLE

a(3) = 2 since 2*3 is perfect.


MATHEMATICA

Table[k = 1; While[DivisorSigma[1, k] >= 2*k  DivisorSigma[1, k*n] < 2*k*n, k++]; k, {n, 2, 100}] (* T. D. Noe, Aug 27 2012 *)


CROSSREFS

Cf. A023196, A005100.
Sequence in context: A323467 A239959 A214435 * A007888 A188723 A077178
Adjacent sequences: A215923 A215924 A215925 * A215927 A215928 A215929


KEYWORD

nonn


AUTHOR

Michel Marcus, Aug 27 2012


STATUS

approved



