A363658 Positive numbers m where A217854(m) is positive and increases to a record.

2, 3, 5, 6, 8, 10, 12, 18, 20, 24, 30, 40, 42, 48, 60, 72, 84, 90, 96, 108, 120, 168, 180, 240, 336, 360, 420, 480, 504, 540, 600, 630, 660, 672, 720, 840, 1080, 1260, 1440, 1680, 2160, 2520, 3360, 3780, 3960, 4200, 4320, 4620, 4680, 5040, 7560, 9240, 10080

Offset: 1

Author

Simon Jensen, Jun 13 2023

Keywords

• nonn

Comments

(-m)^tau(m) > 0 and (-m)^tau(m) > (-k)^tau(k) for all positive k < m, where tau is the number of divisors function.

There are no squares in this sequence.

It appears that if n > 13, then a(n) = A067128(n). See the link.

Only a finite number of terms in A002093 can also be terms in this sequence. See the link.

Examples

			5 is a term since (-5)^tau(5) = (-5)^2 = 25 and 25 > (-k)^tau(k) for k = 1,...,4.
		

Links

• Simon Jensen, Table of n, a(n) for n = 1..135
• Simon Jensen, On an extended divisor product summatory function

Crossrefs

Cf. A363657, A067128, A000005, A002093, A217854, A224914.

Programs

PARI

isok(m) = my(x=(-m)^numdiv(m)); if (x>0, for (k=1, m-1, if (x <= (-k)^numdiv(k), return(0))); return(1)); \\ Michel Marcus, Aug 31 2023