login
A328964
Smallest k such that omega(k) * bigomega(k) = n, where omega = A001221, bigomega = A001222.
9
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
0,2
LINKS
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
EXAMPLE
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)
MATHEMATICA
dat=Table[PrimeOmega[n]*PrimeNu[n], {n, 1000}];
Table[Position[dat, i][[1, 1]], {i, First[Split[Union[dat], #2==#1+1&]]}]
PROG
(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
CROSSREFS
Positions of first appearances in A113901.
Sequence in context: A131886 A265014 A262243 * A061284 A016017 A071571
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 02 2019
EXTENSIONS
More terms from Daniel Suteu, Nov 03 2019
STATUS
approved