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%I #11 Aug 11 2022 08:55:10
%S 27,125,343,625,1331,42875,2197,3125,2401,166375,4913,214375,6859,
%T 274625,456533,15625,12167,300125,24389,831875,753571,614125,29791,
%U 1071875,14641,857375,16807,1373125,50653,57066625,68921,78125,1685159
%N a(1)=27; if n = Product p_i^e_i, n>1, then a(n) = Product p_{i+2}^{e_i+2}.
%C Analog of A045967 a(1)=4; if n = Product p_i^e_i, n>1, then a(n) = Product p_{i+1}^{e_i+1}. In a sense, n is the zeroth sequence in a family of sequences, A045967 is the first sequence in a family of sequences and a(n) is the second sequence in a family of sequences.
%C If we had a(1) = 1 (instead of 4), then this would be multiplicative and a permutation of A353502. - _Amiram Eldar_, Aug 11 2022
%F Sum_{n>=1} 1/a(n) = (72/95)*A065483 - 26/27. - _Amiram Eldar_, Aug 11 2022
%p A126272 := proc(n) local pf,i,p,e,resul ; if n = 1 then 27 ; else pf := ifactors(n)[2] ; resul := 1 ; for i from 1 to nops(pf) do p := op(1,op(i,pf)) ; e := op(2,op(i,pf)) ; resul := resul * nextprime(nextprime(p))^(e+2) ; od ; resul ; fi ; end: for n from 1 to 40 do printf("%d, ",A126272(n)) ; od ; # _R. J. Mathar_, Apr 20 2007
%t f[p_, e_] := NextPrime[p, 2]^(e + 2); a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%Y Cf. A000040, A045967, A065483, A353502.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Mar 09 2007
%E More terms from _R. J. Mathar_, Apr 20 2007
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