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The least number with the same prime factorization pattern (A348717) as A332449(n) = A005940(1+(3*A156552(n))).
4

%I #9 Apr 09 2022 13:26:32

%S 1,4,4,10,4,16,4,30,10,36,4,22,4,100,16,90,4,40,4,250,36,196,4,66,10,

%T 484,30,490,4,64,4,270,100,676,16,154,4,1156,196,750,4,144,4,1210,22,

%U 1444,4,198,10,84,484,1690,4,120,36,1470,676,2116,4,34,4,3364,250,810,100,400,4,2890,1156,324,4,462,4,3844

%N The least number with the same prime factorization pattern (A348717) as A332449(n) = A005940(1+(3*A156552(n))).

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = A348717(A332449(n)) = A332449(A348717(n)).

%o (PARI)

%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };

%o 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 A332449(n) = A005940(1+(3*A156552(n)));

%o 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 A353267(n) = A348717(A332449(n));

%Y Cf. A005940, A156552, A332449, A348717.

%Y Cf. also A305897 (rgs-transform), A352892, A353268.

%K nonn

%O 1,2

%A _Antti Karttunen_, Apr 09 2022