A316570 Multiplicative digital root of sigma(n).

1, 3, 4, 7, 6, 2, 8, 5, 3, 8, 2, 6, 4, 8, 8, 3, 8, 4, 0, 8, 6, 8, 8, 0, 3, 8, 0, 0, 0, 4, 6, 8, 6, 0, 6, 9, 8, 0, 0, 0, 8, 0, 6, 6, 0, 4, 6, 8, 5, 4, 4, 4, 0, 0, 4, 0, 0, 0, 0, 6, 2, 0, 0, 4, 6, 6, 6, 2, 0, 6, 4, 0, 6, 4, 8, 0, 0, 6, 0, 6, 2, 2, 6, 6, 0, 6, 0

Offset: 1

Author

Jaroslav Krizek, Jul 07 2018

Keywords

• nonn
• base

Comments

Multiplicative digital root of A000203(n).

Examples

			For n = 12: sigma(12) = 28; a(n) = 6 because 2 * 8 = 16; 1 * 6 = 6.
		

Crossrefs

Cf. A000203, A031347.

Cf. A190998 (additive digital root of sigma(n)).

Programs

Maple

m:= n-> `if`(n<10, n, m(mul(d, d=convert(n, base, 10)))):
a:= n-> m(numtheory[sigma](n)):
seq(a(n), n=1..100);  # Alois P. Heinz, Jul 21 2018

PARI

a031347(n) = while(n>9, n=prod(i=1, #n=digits(n), n[i])); n;
a(n) = a031347(sigma(n)); \\ Michel Marcus, Jul 07 2018

Formula

a(n) = A031347(A000203(n)).