A378659 Positions of records for ratio A003961(n)/sigma(n), where A003961 is fully multiplicative with a(p) = nextprime(p) and sigma is the sum of the divisors function.

1, 3, 4, 7, 8, 9, 16, 27, 32, 64, 128, 243, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864

Offset: 1

Author

Antti Karttunen, Dec 06 2024

Keywords

• nonn

Examples

			  Term k       A003961(k)/A000203(k)    ratio
       1                1/1          =  1
       3                5/4          =  1.25
       4                9/7          =  1.2857143
       7               11/8          =  1.375
       8               27/15         =  1.8
       9               25/13         =  1.9230769
      16               81/31         =  2.6129032
      27              125/40         =  3.125
      32              243/63         =  3.8571429
      64              729/127        =  5.7401575
     128             2187/255        =  8.5764706
     243             3125/364        =  8.5851648
     256             6561/511        =  12.839530
     ...
33554432     847288609443/67108863   =  12625.584
67108864    2541865828329/134217727  =  18938.376
		

Links

• Index entries for sequences related to prime indices in the factorization of n
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961.

Cf. A001359 (apparently gives the positions of successive minima of the ratio, for n > 2).

Cf. also A341529, A349627, A349628, A354827, A354828.