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A353268 The least number with the same prime factorization pattern (A348717) as A329603(n) = A005940(1+(1+(3*A156552(n)))).

%I A353268 #6 Apr 09 2022 14:59:18
%S A353268 2,2,8,6,18,2,50,12,20,8,98,14,242,18,32,24,338,6,578,54,72,50,722,28,
%T A353268 42,98,60,150,1058,2,1682,48,200,242,162,70,1922,338,392,108,2738,8,
%U A353268 3362,294,44,578,3698,56,110,20,968,726,4418,12,450,300,1352,722,5618,26,6962,1058,500,96,882,18,7442,1014,2312
%N A353268 The least number with the same prime factorization pattern (A348717) as A329603(n) = A005940(1+(1+(3*A156552(n)))).
%H A353268 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A353268 a(n) = A348717(A329603(n)).
%F A353268 For all n >= 1, a(2n) = A352892(2n), a(2n-1) = A329603(2n-1).
%o A353268 (PARI)
%o A353268 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A353268 A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
%o A353268 A329603(n) = A005940(2+(3*A156552(n)));
%o A353268 A348717(n) = { my(f=factor(n)); if(#f~>0, my(pi1=primepi(f[1, 1])); for(k=1, #f~, f[k, 1] = prime(primepi(f[k, 1])-pi1+1))); factorback(f); }; \\ From A348717
%o A353268 A353268(n) = A348717(A329603(n));
%Y A353268 Cf. A005940, A156552, A348717, A353267.
%Y A353268 Coincides with A352892 on even n, and with A329603 on odd n.
%K A353268 nonn
%O A353268 1,1
%A A353268 _Antti Karttunen_, Apr 09 2022