A393013 Numbers k with the property sigma(k)/k >= 6 that are not divisible by any other number with that property, where sigma = A000203.

130429015516800, 139424120035200, 144403552893600, 172352627647200, 195643523275200, 209136180052800, 249614150385600, 293465284912800, 326072538792000, 348560300088000, 368478031521600, 381970688299200, 400603404801600, 408313494388800, 428231225822400, 437868837806400

Offset

1,1

Comments

This sequence is an exact equivalent of A006039 (the primitive nondeficient numbers), the difference being A006039 requires the abundancy ratio, sigma(k)/k, to be at least 2, whereas here we use 6. - Peter Munn, Feb 12 2026

The term with the greatest abundancy ratio is 204773655626139600 = A307111(6). - Peter Munn, Jun 05 2026

Links

Table of n, a(n) for n=1..16.

Eric Weisstein's World of Mathematics, Abundancy.

Formula

{a(n)} = {k >= 2 : A000203(k) >= 6k and A000203(A395192(k)) < 6*A395192(k)}. - Peter Munn, Jun 05 2026

Example

130429015516800 is in the sequence as sigma(130429015516800)/130429015516800 >= 6 but none of its divisors d has sigma(d)/d >= 6.

Prog

(PARI) is(n) = {my(f = factor(n)); if(sigma(f) < 6*n, return(0)); for(i = 1, #f~, c = n\f[i, 1]; if(sigma(c) >= 6*c, return(0))); 1}

Crossrefs

Cf. A000203, A307111, A395192.

For equivalent sets of primitives for other abundancy ratios see A006039, A388019 (and its CROSSREFS), A392936.

Sequence in context: A053852 A234074 A384780 * A175347 A216405 A364412

Adjacent sequences: A393010 A393011 A393012 * A393014 A393015 A393016

Keyword

nonn,changed

Author

David A. Corneth, Jan 30 2026

Status

approved