A114809 Smallest abundant number with some prime powers fixed by n.

12, 945, 20, 18, 12, 5391411025, 12, 12, 12, 81081, 12, 70, 12, 6435, 56, 24, 12, 5775, 12, 18, 20, 945, 12, 20, 20, 945, 18, 18, 12, 20169691981106018776756331, 12, 48, 20, 945, 12, 30, 12, 945, 20, 12, 12, 366005822969340125, 12, 18, 12, 945

Offset: 1

Author

Hugo van der Sanden, Feb 09 2006

Keywords

• nonn

Comments

If n = prod{ p_i^x_i }, a(n) = prod{ p_i^y_i } then we require y_i = x_i - 1 whenever x_i > 0.

Same as A114371 for squarefree n.

If k is abundant then k = a(k * prod{ p | k }).

Examples

			12 = 2^2.3^1, so a(12)=70 is the least abundant 2^1.3^0.k with (k,2.3)=1.
		

Crossrefs

Cf. A005101, A005231, A047802, A114371.