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

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences computed from indices in prime factorization

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)

Prog

(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)));

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.

Sequence in context: A244863 A077584 A093896 * A191905 A113432 A129830

Adjacent sequences: A332446 A332447 A332448 * A332450 A332451 A332452

Keyword

nonn

Author

Antti Karttunen, Feb 14 2020

Status

approved