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 A048767 If n = Product (p_j^k_j) then a(n) = Product ( prime(k_j)^pi(p_j) ) where pi is A000720. 12
 1, 2, 4, 3, 8, 8, 16, 5, 9, 16, 32, 12, 64, 32, 32, 7, 128, 18, 256, 24, 64, 64, 512, 20, 27, 128, 25, 48, 1024, 64, 2048, 11, 128, 256, 128, 27, 4096, 512, 256, 40, 8192, 128, 16384, 96, 72, 1024, 32768, 28, 81, 54, 512, 192, 65536, 50, 256, 80, 1024, 2048 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If the prime power factors p^e of n are replaced by prime(e)^pi(p), then the prime terms q in the sequence pertain to 2^m with m > 1, since pi(2) = 1. - Michael De Vlieger, Apr 25 2017 Also the Heinz number of the integer partition obtained by applying the map described in A217605 (which interchanges the parts with their multiplicities) to the integer partition with Heinz number n, where the Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). The image of this map (which is the union of this sequence) is A130091. - Gus Wiseman, May 04 2019 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 Stephan Wagner, The Number of Fixed Points of Wilf's Partition Involution, The Electronic Journal of Combinatorics, 20(4) (2013), #P13. EXAMPLE For n=6, 6 = (2^1)*(3^1), a(6) = ([first prime]^pi(2))*([first prime]^pi(3)) = (2^1)*(2^2) = 8. From Gus Wiseman, May 04 2019: (Start) For n = 1..20, the prime indices of n together with the prime indices of a(n) are the following: 1: {} {} 2: {1} {1} 3: {2} {1,1} 4: {1,1} {2} 5: {3} {1,1,1} 6: {1,2} {1,1,1} 7: {4} {1,1,1,1} 8: {1,1,1} {3} 9: {2,2} {2,2} 10: {1,3} {1,1,1,1} 11: {5} {1,1,1,1,1} 12: {1,1,2} {1,1,2} 13: {6} {1,1,1,1,1,1} 14: {1,4} {1,1,1,1,1} 15: {2,3} {1,1,1,1,1} 16: {1,1,1,1} {4} 17: {7} {1,1,1,1,1,1,1} 18: {1,2,2} {1,2,2} 19: {8} {1,1,1,1,1,1,1,1} 20: {1,1,3} {1,1,1,2} (End) MAPLE A048767 := proc(n) local a, p, e, f; a := 1 ; for f in ifactors(n)[2] do p := op(1, f) ; e := op(2, f) ; a := a*ithprime(e)^numtheory[pi](p) ; end do: a ; end proc: # R. J. Mathar, Nov 08 2012 MATHEMATICA Table[{p, k} = Transpose@ FactorInteger[n]; Times @@ (Prime[k]^PrimePi[p]), {n, 58}] (* Ivan Neretin, Jun 02 2016 *) Array[Apply[Times, FactorInteger[#] /. {p_, e_} /; e >= 0 :> Prime[e]^PrimePi[p]] &, 65] (* Michael De Vlieger, Apr 25 2017 *) CROSSREFS Cf. A008477, A048768, A048769, A064988. Cf. A056239, A098859, A109298, A112798, A118914, A130091, A217605, A320348, A325326, A325337. Sequence in context: A209406 A188706 A304408 * A269851 A284457 A182944 Adjacent sequences: A048764 A048765 A048766 * A048768 A048769 A048770 KEYWORD easy,nonn,mult AUTHOR Naohiro Nomoto EXTENSIONS a(1)=1 prepended by Alois P. Heinz, Jul 26 2015 STATUS approved

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Last modified June 6 05:06 EDT 2023. Contains 363139 sequences. (Running on oeis4.)