A323406 Greatest common divisor of Product (p_i^e_i)-1 and Product (p_i^e_i)+1, when n = Product (p_i^e_i): a(n) = gcd(A047994(n), A034448(n)).

1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 6, 8, 1, 2, 2, 2, 6, 4, 2, 2, 2, 2, 6, 2, 2, 2, 8, 2, 1, 4, 2, 24, 2, 2, 6, 8, 2, 2, 12, 2, 30, 4, 2, 2, 2, 2, 6, 8, 2, 2, 2, 8, 6, 4, 2, 2, 24, 2, 6, 16, 1, 12, 4, 2, 6, 4, 24, 2, 2, 2, 6, 8, 2, 12, 24, 2, 6, 2, 2, 2, 4, 4, 6, 8, 2, 2, 4, 8, 6, 4, 2, 24, 2, 2, 6, 40, 2, 2, 8, 2, 42, 48

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Formula

a(n) = gcd(A034448(n), A047994(n)), where A034448 is unitary sigma, and A047994 is unitary phi.

Prog

(PARI)
A047994(n) = { my(f=factor(n)~); prod(i=1, #f, f[1, i]^f[2, i]-1); };
A034448(n) = { my(f=factor(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448
A323406(n) = gcd(A034448(n), A047994(n));

Crossrefs

Cf. A034448, A047994.

Cf. also A009223, A066086, A126865, A322362, A323166, A323409.

Sequence in context: A193523 A092505 A066086 * A160520 A235708 A353929

Adjacent sequences: A323403 A323404 A323405 * A323407 A323408 A323409

Keyword

nonn

Author

Antti Karttunen, Jan 15 2019

Status

approved