A292113 List of numbers n such that A039654(n) reaches a new record high.

2, 3, 4, 8, 9, 32, 36, 64, 81, 100, 121, 144, 228, 256, 300, 400, 441, 468, 800, 1200, 2964, 5202, 5408, 6084, 6400, 7500, 8100, 9216, 24556, 28092, 31329, 32176, 32400, 37296, 49017, 49152, 57600, 72156, 80400, 83161, 86352, 88200, 133200

Offset: 1

Author

N. J. A. Sloane, Sep 22 2017

Keywords

• nonn

Comments

Naively, one might have expected these numbers to have some other distinguishing property (primorials, perhaps), but that seems not to be the case.

Except for 3 of the listed terms, a(n)-1 or a(n)+1 has at most 2 prime divisors. The same is true for many of the terms themselves, often of the form 2^k, 3^k, 2^k*3^k' or 2^k*5^k'. (Factorization of the terms: 2, 3, 2^2, 2^3, 3^2, 2^5, 2^2*3^2, 2^6, 3^4, 2^2*5^2, 11^2, 2^4*3^2, 2^2*3*19, 2^8, 2^2*3*5^2, 2^4*5^2, 3^2*7^2, 2^2*3^2*13, 2^5*5^2, ...) - M. F. Hasler, Sep 25 2017

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..56

Crossrefs

Cf. A039654, A039655, A292112.

Programs

PARI

m=-n=1; until(print1(n","), until(A039654(n++)>m,); m=A039654(n)) \\ M. F. Hasler, Sep 25 2017