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%I #7 May 23 2022 17:45:43
%S 1,5,7,25,13,35,11,125,49,65,19,175,17,55,91,625,29,245,23,325,77,95,
%T 31,875,169,85,343,275,37,455,43,3125,133,145,143,1225,41,115,119,
%U 1625,53,385,47,475,637,155,59,4375,121,845,203,425,61,1715,247,1375,161,185,67,2275,73,215,539,15625,221,665,71,725
%N Fully multiplicative with a(p^e) = A354200(A000720(p))^e.
%C Permutation of A007310. Preserves the prime signature.
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%o (PARI)
%o A354200(n) = if(1==n,5,my(p=prime(n), m=p%4); forprime(q=1+p,,if(m==(q%4),return(q))));
%o A354202(n) = { my(f=factor(n)); for(k=1,#f~,f[k,1] = A354200(primepi(f[k,1]))); factorback(f); };
%Y Cf. A007310 (terms sorted into ascending order), A354200, A354203 (left inverse), A354204 (Möbius transform), A354205 (inverse Möbius transform).
%Y Cf. also A003961, A108548, A267099, A332818, A348746, A354091 for similar constructions.
%K nonn,mult
%O 1,2
%A _Antti Karttunen_, May 23 2022