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Smallest k such that omega(k) * bigomega(k) = n, where omega = A001221, bigomega = A001222.
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%I #22 Feb 12 2022 20:28:52

%S 1,2,4,8,6,32,12,128,24,30,48,2048,60,8192,192,120,210,131072,240,

%T 524288,420,480,3072,8388608,840,2310,12288,1920,1680,536870912,3840,

%U 2147483648,3360,7680,196608,9240,6720,137438953472,786432,30720,13440,2199023255552,60060,8796093022208

%N Smallest k such that omega(k) * bigomega(k) = n, where omega = A001221, bigomega = A001222.

%H Andrew Howroyd, <a href="/A328964/b328964.txt">Table of n, a(n) for n = 0..1000</a>

%F a(p) = 2^p, for p prime. - _Daniel Suteu_, Nov 03 2019

%F a(n) = min_{d|n, d<=n/d} 2^(n/d-d)*A002110(d) for n > 0. - _Andrew Howroyd_, Nov 04 2019

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

%e 1: ()

%e 2: (1)

%e 4: (2)

%e 8: (3)

%e 6: (1,1)

%e 32: (5)

%e 12: (2,1)

%e 128: (7)

%e 24: (3,1)

%e 30: (1,1,1)

%e 48: (4,1)

%e 2048: (11)

%e 60: (2,1,1)

%e 8192: (13)

%e 192: (6,1)

%e 120: (3,1,1)

%e 210: (1,1,1,1)

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

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

%o (PARI) a(n)={if(n<1, 1, my(m=oo); fordiv(n, d, if(d<=n/d, m=min(m, 2^(n/d-d)*vecprod(primes(d))))); m)} \\ _Andrew Howroyd_, Nov 04 2019

%Y Positions of first appearances in A113901.

%Y Cf. A001221, A001222, A002110, A025487, A124010, A307409, A320632, A323023, A328956, A328958, A328959, A328962, A328963, A328965.

%K nonn

%O 0,2

%A _Gus Wiseman_, Nov 02 2019

%E More terms from _Daniel Suteu_, Nov 03 2019