A332449 a(n) = A005940(1+(3*A156552(n))).

1, 4, 9, 10, 25, 16, 49, 30, 21, 36, 121, 22, 169, 100, 81, 90, 289, 40, 361, 250, 225, 196, 529, 66, 55, 484, 105, 490, 841, 64, 961, 270, 441, 676, 625, 154, 1369, 1156, 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

Offset: 1

Author

Antti Karttunen, Feb 14 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A329609 (terms sorted into ascending order).

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.

Cf. also A332223.

Programs

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
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
A332449(n) = A005940(1+(3*A156552(n)));

Formula

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

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

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

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

From Antti Karttunen, Apr 10 2022: (Start)

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

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

(End)