A277216 Product of decimal digits of sum of divisors of n.

1, 3, 4, 7, 6, 2, 8, 5, 3, 8, 2, 16, 4, 8, 8, 3, 8, 27, 0, 8, 6, 18, 8, 0, 3, 8, 0, 30, 0, 14, 6, 18, 32, 20, 32, 9, 24, 0, 30, 0, 8, 54, 16, 32, 56, 14, 32, 8, 35, 27, 14, 72, 20, 0, 14, 0, 0, 0, 0, 48, 12, 54, 0, 14, 32, 16, 48, 12, 54, 16, 14, 45, 28, 4, 8

Offset: 1

Author

Jaroslav Krizek, Oct 05 2016

Keywords

• nonn
• base

Comments

Conjecture: a(n) = n only for numbers 1 and 210; sigma(210) = 576; a(210) = 5*7*6 = 210.

Examples

			a(12) = 16 because sigma(12) = 28; 2*8 = 16.
		

Links

• Jaroslav Krizek, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A067342 (sum of decimal digits of sigma(n)).

Cf. A000203, A007954, A277217.

Programs

Magma

[&*Intseq(SumOfDivisors(n)): n in [1..100000]];

Maple

seq( convert(convert(numtheory:-sigma(n),base,10),`*`), n=1..100); # Robert Israel, Oct 06 2016

Mathematica

Table[Times @@ IntegerDigits@ DivisorSigma[1, n], {n, 75}] (* Michael De Vlieger, Oct 06 2016 *)

PARI

a(n) = d = digits(sigma(n)); prod(k=1, #d, d[k]); \\ Michel Marcus, Oct 05 2016

Formula

a(n) = A007954(A000203(n)).