

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.


2



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
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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 A006549 A134459
Adjacent sequences: A239970 A239971 A239972 * A239974 A239975 A239976


KEYWORD

nonn


AUTHOR

Michel Marcus, Mar 30 2014


STATUS

approved



