A353790 a(n) = A353749(sigma(A003961(n))), where A353749(k) = phi(k) * A064989(k), and A064989 shifts the prime factorization one step towards lower primes, while A003961 shifts the factorization one step towards higher primes.

1, 2, 4, 132, 4, 16, 8, 48, 870, 16, 30, 528, 24, 32, 32, 5390, 24, 1740, 16, 528, 96, 120, 48, 384, 1224, 96, 1056, 1056, 16, 128, 306, 7920, 240, 96, 64, 114840, 120, 64, 288, 384, 140, 384, 32, 3960, 3480, 192, 144, 21560, 9180, 2448, 192, 3168, 96, 4224, 240, 768, 192, 64, 870, 4224, 416, 1224, 6960, 1191372, 192

Offset

1,2

Comments

See comments in A353789.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = A353750(A003961(n)) = A326042(n) * A353767(n).

a(n) = A000010(A003973(n)) * A064989(A003973(n)).

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A064989(n) = { my(f=factor(n>>valuation(n, 2))); for(i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f); };
A353790(n) = { my(s=sigma(A003961(n))); (eulerphi(s)*A064989(s)); };

Crossrefs

Cf. A003961, A003973, A064989, A326042, A353750, A353767, A353789.

Cf. also A353794.

Sequence in context: A012617 A012614 A018500 * A271677 A226070 A013552

Adjacent sequences: A353787 A353788 A353789 * A353791 A353792 A353793

Keyword

nonn

Author

Antti Karttunen, May 10 2022

Status

approved