A328964 Smallest k such that omega(k) * bigomega(k) = n, where omega = A001221, bigomega = A001222.

1, 2, 4, 8, 6, 32, 12, 128, 24, 30, 48, 2048, 60, 8192, 192, 120, 210, 131072, 240, 524288, 420, 480, 3072, 8388608, 840, 2310, 12288, 1920, 1680, 536870912, 3840, 2147483648, 3360, 7680, 196608, 9240, 6720, 137438953472, 786432, 30720, 13440, 2199023255552, 60060, 8796093022208

Offset: 0

Author

Gus Wiseman, Nov 02 2019

Keywords

• nonn

Examples

			The sequence of terms together with their prime signatures begins:
     1: ()
     2: (1)
     4: (2)
     8: (3)
     6: (1,1)
    32: (5)
    12: (2,1)
   128: (7)
    24: (3,1)
    30: (1,1,1)
    48: (4,1)
  2048: (11)
    60: (2,1,1)
  8192: (13)
   192: (6,1)
   120: (3,1,1)
   210: (1,1,1,1)
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000

Crossrefs

Positions of first appearances in A113901.

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

Programs

Mathematica

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

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

Formula

a(p) = 2^p, for p prime. - Daniel Suteu, Nov 03 2019

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

Extensions

More terms from Daniel Suteu, Nov 03 2019