A332449 - OEIS

%I #23 Apr 11 2022 20:48:07

%S 1,4,9,10,25,16,49,30,21,36,121,22,169,100,81,90,289,40,361,250,225,

%T 196,529,66,55,484,105,490,841,64,961,270,441,676,625,154,1369,1156,

%U 1089,750,1681,144,1849,1210,39,1444,2209,198,91,84,1521,1690,2809,120,1225,1470,2601,2116,3481,34,3721,3364,1029,810,3025,400

%N a(n) = A005940(1+(3*A156552(n))).

%H Antti Karttunen, <a href="/A332449/b332449.txt">Table of n, a(n) for n = 1..16384</a>

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

%F a(n) = A005940(1+(3*A156552(n))).

%F a(p) = p^2 for all primes p.

%F a(u) = A332451(u) and A010052(a(u)) = 1 for all squarefree numbers (A005117).

%F a(A003961(n)) = A003961(a(n)) = A005940(1+(6*A156552(n))).

%F From _Antti Karttunen_, Apr 10 2022: (Start)

%F a(n) = A347119(n) * A000290(A347120(n)) = A353270(n) * A353272(n).

%F a(A353269(n)) = 1 for all n.

%F (End)

%o (PARI)

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

%o A156552(n) = {my(f = factor(n), 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}; \\ From A156552

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

%Y Cf. A329609 (terms sorted into ascending order).

%Y Cf. A000290, A003961, A005117 (positions of squares), A005940, A010052, A156552, A277010, A329603, A332450, A332451, A347119, A347120, A353267 [= A348717(a(n))], A353269, A353270 [= gcd(n, a(n))], A353271, A353272, A353273.

%Y Cf. also A332223.

%K nonn

%O 1,2

%A _Antti Karttunen_, Feb 14 2020