A215926 Smallest deficient number k such that the product k*n is non-deficient (perfect or abundant).

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

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: A341097 A239959 A214435 * A007888 A188723 A341890

Adjacent sequences: A215923 A215924 A215925 * A215927 A215928 A215929

Keyword

nonn

Author

Michel Marcus, Aug 27 2012

Status

approved