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

Author

Antti Karttunen, May 10 2022

Keywords

• nonn

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)

Crossrefs

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

Cf. also A353794.

Programs

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)); };

Formula

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

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