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%I #35 Oct 29 2022 09:16:00
%S 3,5,7,25,11,35,13,125,49,55,17,175,19,65,77,625,23,245,29,275,91,85,
%T 31,875,121,95,343,325,37,385,41,3125,119,115,143,1225,43,145,133,
%U 1375,47,455,53,425,539,155,59,4375,169,605,161,475,61,1715,187,1625,203,185,67
%N a(1)=3; if n = Product p_i^e_i, n > 1, then a(n) = Product p_{i+2}^e_i.
%C If we had a(1) = 1 (instead of 3), then this would be fully multiplicative with a(prime(k)) = prime(k+2) (see A357852). - _Antti Karttunen_, Jan 10 2020
%D From a puzzle proposed by _Marc LeBrun_.
%H Reinhard Zumkeller, <a href="/A045966/b045966.txt">Table of n, a(n) for n = 1..10000</a>
%F From _Peter Munn_, Dec 27 2019, for n >= 2, k >= 2: (Start)
%F a(n) = A003961^2(n).
%F a(n^k) = a(n)^k.
%F a(A003961(n)) = A003961(a(n)).
%F a(A059896(n,k)) = A059896(a(n), a(k)).
%F (End)
%t a[1] = 3; a[n_] := With[{f = FactorInteger[n]}, Times @@ (Prime[PrimePi[f[[All, 1]]]+2]^f[[All, 2]])]; Array[a, 60] (* _Jean-François Alcover_, Jun 19 2015 *)
%o (Haskell)
%o a045966 1 = 3
%o a045966 n = product $ zipWith (^)
%o (map a101300 $ a027748_row n) (a124010_row n)
%o -- _Reinhard Zumkeller_, Jun 03 2013, Dec 23 2011
%o (PARI) A045966(n) = if(1==n,3,my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(1+nextprime(1+f[i, 1]))); factorback(f)); \\ _Antti Karttunen_, Jan 10 2020
%Y See A027748, A124010 for factorization data for n.
%Y Cf. A000040, A003961, A101300.
%Y Sequences with similar definitions: A045967, A045968, A045970, A126272.
%Y A059896 is used to express relationship between terms of this sequence.
%Y A357852 is a slightly better version. - _N. J. A. Sloane_, Oct 29 2022
%K easy,nonn,nice
%O 1,1
%A _N. J. A. Sloane_
%E More terms from _David W. Wilson_
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