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 A328965 Smallest k such that (bigomega(k) - 1) * omega(k) = n, and 0 if none exists, where omega = A001221, bigomega = A001222. 10
 1, 4, 6, 16, 12, 64, 24, 256, 48, 60, 96, 4096, 120, 16384, 384, 240, 420, 262144, 480, 1048576, 840, 960, 6144, 16777216, 1680, 4620, 24576, 3840, 3360, 1073741824, 7680, 4294967296, 6720, 15360, 393216, 18480, 13440, 274877906944, 1572864, 61440, 26880, 4398046511104 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For n > 0, a(n) is of the form 2^k*primorial(d) where d is a divisor of n and k = n / d - d + 1.  a(n) is never 0 since A307409(2^(n+1)) = n. - Andrew Howroyd, Nov 04 2019 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..1000 FORMULA From Andrew Howroyd, Nov 03 2019: (Start) a(p) = 2^(p + 1) for odd prime p. a(n) = min_{d|n, d<=n/d+1} 2^(n/d-d+1)*A002110(d) for n > 0. (End) EXAMPLE The sequence of terms together with their prime signatures begins:       1: ()       4: (2)       6: (1,1)      16: (4)      12: (2,1)      64: (6)      24: (3,1)     256: (8)      48: (4,1)      60: (2,1,1)      96: (5,1)    4096: (12)     120: (3,1,1)   16384: (14)     384: (7,1)     240: (4,1,1)     420: (2,1,1,1) MATHEMATICA dat=Table[(PrimeOmega[n]-1)*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+1, m=min(m, 2^(n/d-d+1)*vecprod(primes(d))))); m)} \\ Andrew Howroyd, Nov 04 2019 CROSSREFS Positions of first appearances in A307409. Cf. A001221, A001222, A002110, A113901, A124010, A320632, A323023, A328956, A328958, A328959, A328962, A328963, A328964. Sequence in context: A062955 A174932 A278239 * A133092 A240034 A302122 Adjacent sequences:  A328962 A328963 A328964 * A328966 A328967 A328968 KEYWORD nonn AUTHOR Gus Wiseman, Nov 02 2019 EXTENSIONS Terms a(23) and beyond from Andrew Howroyd, Nov 03 2019 STATUS approved

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Last modified September 26 20:36 EDT 2020. Contains 337374 sequences. (Running on oeis4.)