A277216 - OEIS

%I #12 Sep 08 2022 08:46:17

%S 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,

%T 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,

%U 0,0,0,48,12,54,0,14,32,16,48,12,54,16,14,45,28,4,8

%N Product of decimal digits of sum of divisors of n.

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

%H Jaroslav Krizek, <a href="/A277216/b277216.txt">Table of n, a(n) for n = 1..1000</a>

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

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

%p seq( convert(convert(numtheory:-sigma(n),base,10),`*`), n=1..100); # _Robert Israel_, Oct 06 2016

%t Table[Times @@ IntegerDigits@ DivisorSigma[1, n], {n, 75}] (* _Michael De Vlieger_, Oct 06 2016 *)

%o (Magma) [&*Intseq(SumOfDivisors(n)): n in [1..100000]]

%o (PARI) a(n) = d = digits(sigma(n)); prod(k=1, #d, d[k]); \\ _Michel Marcus_, Oct 05 2016

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

%Y Cf. A000203, A007954, A277217.

%K nonn,base

%O 1,2

%A _Jaroslav Krizek_, Oct 05 2016