A239973 Sequence, starting with 1, of increasing numbers such that both the numerator and the denominator of the abundancy index, sigma(n)/n are strictly increasing.

1, 2, 3, 4, 7, 8, 16, 21, 27, 32, 36, 50, 63, 64, 93, 98, 100, 128, 144, 256, 324, 392, 400, 512, 576, 784, 800, 900, 1296, 1600, 1936, 2304, 2916, 3600, 5184, 6400, 7744, 8100, 9216, 10404, 11664, 14400, 17424, 19600, 20736, 22500, 30276, 32400, 41616, 46656

Offset

1,2

Comments

Records of A239972.

Recall that the abundancy index of n is defined as sigma(n)/n with sigma(n) being the sum of divisors of n (A000203). The numerators and denominators of the abundancy index can be found in A017665 and A017666.

It appears that all terms belong to A014567, numbers such that sigma(n) and n are coprime.

Odd terms begin: 1, 3, 7, 21, 27, 63, 93; and no others were found up to 10^7. What is the next odd number, or is 93 the last odd number in the sequence?

Links

Michel Marcus, Table of n, a(n) for n = 1..254

Eric Weisstein's World of Mathematics, Abundancy

Prog

(PARI) lista(nn) = {num = 0; den = 0; for (n = 1, nn, ab = sigma(n)/n; nab = numerator(ab); dab = denominator(ab); if ((nab > num) && (dab > den), print1(n, ", "); num = nab; den = dab; ); ); }

Crossrefs

Cf. A000203, A017665, A017666, A239972.

Sequence in context: A007497 A126882 A333801 * A281782 A334020 A006549

Adjacent sequences: A239970 A239971 A239972 * A239974 A239975 A239976

Keyword

nonn

Author

Michel Marcus, Mar 30 2014

Status

approved