A331613 Odd exceptional numbers: odd k such that A005179(k) < A037019(k).

243, 729, 1215, 2187, 3645, 6561, 10935, 15309, 19683, 32805, 45927, 54675, 59049, 98415, 137781, 164025, 177147, 216513, 255879, 273375, 295245, 334611, 373977, 413343, 452709, 492075, 531441, 570807, 610173, 649539, 688905, 728271, 767637, 807003, 820125, 846369, 885735, 925101

Offset

1,1

Comments

This sequence is infinite, because 3^p is a term for all p >= 5.

It seems that the smallest p-rough exceptional number (i.e., the smallest exceptional number whose smallest prime factor is p) is p^k, where k is the smallest number such that prime(k) > 2^p (p = 2 gives 2^3 = 8, p = 3 gives 3^5 = 243, p = 5 gives 5^12 = 244140625, ...).

Links

Table of n, a(n) for n=1..38.

M. E. Grost, The smallest number with a given number of divisors, Amer. Math. Monthly, 75 (1968), 725-729.

Example

The smallest number with 243 divisors is 2^8 * 3^2 * 5^2 * 7^2 = 2822400, while A037019(243) = 2^2 * 3^2 * 5^2 * 7^2 * 11^2 = 5336100 > A005719(243), so 243 is a term.

Prog

(PARI) isA331613(n) = (n%2) && A037019(n) > A005179(n) \\ See A005179 and A037019 for their programs

Crossrefs

Cf. A072066 (exceptional numbers), A005179, A037019.

Sequence in context: A340757 A255111 A353320 * A255626 A205049 A235540

Adjacent sequences: A331610 A331611 A331612 * A331614 A331615 A331616

Keyword

nonn

Author

Jianing Song, Jan 22 2020

Status

approved