The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A331613 Odd exceptional numbers: odd k such that A005179(k) < A037019(k). 0
 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 (list; graph; refs; listen; history; text; internal format)
 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 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: A232924 A067838 A255111 * A255626 A205049 A235540 Adjacent sequences:  A331610 A331611 A331612 * A331614 A331615 A331616 KEYWORD nonn AUTHOR Jianing Song, Jan 22 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 26 09:38 EST 2020. Contains 338639 sequences. (Running on oeis4.)