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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.
6

%I #6 Nov 03 2019 19:50:36

%S 30,6,1,72,144,216,576,360,2304,840,720,1728,1080,1260,147456,6912,

%T 1800,2160,2359296,4620,9437184,2520,3600,110592,6480,5400,46656,6300,

%U 7200,5040,9240,12960,17280,7560,10800,7077888,186624,10080,13860

%N 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.

%e The sequence of terms together with their prime signatures begins:

%e 30: (1,1,1)

%e 6: (1,1)

%e 1: ()

%e 72: (3,2)

%e 144: (4,2)

%e 216: (3,3)

%e 576: (6,2)

%e 360: (3,2,1)

%e 2304: (8,2)

%e 840: (3,1,1,1)

%e 720: (4,2,1)

%e 1728: (6,3)

%e 1080: (3,3,1)

%e 1260: (2,2,1,1)

%e 147456: (14,2)

%e 6912: (8,3)

%e 1800: (3,2,2)

%e 2160: (4,3,1)

%t dat=Table[DivisorSigma[0,n]-PrimeOmega[n]*PrimeNu[n],{n,1000}];

%t Table[Position[dat,i][[1,1]],{i,First[Split[Union[dat],#2==#1+1&]]}]

%Y Positions of first appearances in A328958.

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

%K nonn

%O -1,1

%A _Gus Wiseman_, Nov 02 2019