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A003961
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Fully multiplicative with a(p(k)) = p(k+1) for k-th prime p(k).
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14
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1, 3, 5, 9, 7, 15, 11, 27, 25, 21, 13, 45, 17, 33, 35, 81, 19, 75, 23, 63, 55, 39, 29, 135, 49, 51, 125, 99, 31, 105, 37, 243, 65, 57, 77, 225, 41, 69, 85, 189, 43, 165, 47, 117, 175, 87, 53, 405, 121, 147, 95, 153, 59, 375, 91, 297, 115, 93, 61, 315, 67, 111, 275, 729, 119
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) is odd for all n and for each odd m there exists a k with a(k) = m (see A064216). a(n) > n for n > 1: bijection between the odd and all numbers. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 26 2001
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
| If n = Product p(k)^e(k) then a(n) = Product p(k+1)^e(k).
Multiplicative with a(p^e) = A000040(A000720(p)+1)^e. - David W. Wilson (davidwwilson(AT)comcast.net), Aug 01, 2001.
a(n)=product(A000040(A049084(A027748(n,k)+1))^A124010(n,k):k=1..A001221(n)). [Reinhard Zumkeller, Oct 09 2011]
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EXAMPLE
| a(12) = a(2^2 * 3) = a(prime(1)^2 * prime(2)) = prime(2)^2 * prime(3) = 3^2 * 5 = 45. a(A002110(n)) = A002110(n + 1) / 2.
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MATHEMATICA
| a[p_?PrimeQ] := a[p] = Prime[ PrimePi[p] + 1]; a[1] = 1; a[n_] := a[n] = Times @@ ( a[First[#]] ^ Last[#] & ) /@ FactorInteger[n]; Table[ a[n], {n, 1, 65}] (* From Jean-François Alcover, Dec 01 2011 *)
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PROG
| (PARI) a(n)=local(f); if(n<1, 0, f=factor(n); prod(k=1, matsize(f)[1], nextprime(1+f[k, 1])^f[k, 2]))
(Haskell)
a003961 n = product $ zipWith (^) (shiftPrimes n) (a124010_row n) where
shiftPrimes = map (a000040 . (+ 1) . a049084) . a027748_row
-- Reinhard Zumkeller, Oct 09 2011
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CROSSREFS
| See A045965 for another version. Cf. A064216, A000040, A002110, A000265.
Sequence in context: A079427 A168271 A081761 * A100463 A166722 A094549
Adjacent sequences: A003958 A003959 A003960 * A003962 A003963 A003964
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KEYWORD
| nonn,mult,nice
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AUTHOR
| Marc LeBrun (mlb(AT)well.com)
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