A328962 Smallest k such that sigma_0(k) - omega(k) * nu(k) = n, and 0 if none exists, where sigma_0 = A000005, nu = A001221, omega = A001222.

30, 6, 1, 72, 144, 216, 576, 360, 2304, 840, 720, 1728, 1080, 1260, 147456, 6912, 1800, 2160, 2359296, 4620, 9437184, 2520, 3600, 110592, 6480, 5400, 46656, 6300, 7200, 5040, 9240, 12960, 17280, 7560, 10800, 7077888, 186624, 10080, 13860

Offset

-1,1

Links

Table of n, a(n) for n=-1..37.

Example

The sequence of terms together with their prime signatures begins:
      30: (1,1,1)
       6: (1,1)
       1: ()
      72: (3,2)
     144: (4,2)
     216: (3,3)
     576: (6,2)
     360: (3,2,1)
    2304: (8,2)
     840: (3,1,1,1)
     720: (4,2,1)
    1728: (6,3)
    1080: (3,3,1)
    1260: (2,2,1,1)
  147456: (14,2)
    6912: (8,3)
    1800: (3,2,2)
    2160: (4,3,1)

Mathematica

dat=Table[DivisorSigma[0, n]-PrimeOmega[n]*PrimeNu[n], {n, 1000}];
Table[Position[dat, i][[1, 1]], {i, First[Split[Union[dat], #2==#1+1&]]}]

Crossrefs

Positions of first appearances in A328958.

Cf. A000005, A001221, A001222, A113901, A124010, A307409, A320632, A323023, A328956, A328959, A328963, A328964, A328965.

Sequence in context: A255865 A299195 A040878 * A073460 A036390 A040879

Adjacent sequences: A328959 A328960 A328961 * A328963 A328964 A328965

Keyword

nonn

Author

Gus Wiseman, Nov 02 2019

Status

approved