A277217 Numbers k for which the sum of digits of sigma(k) = the product of digits of sigma(k).

1, 2, 3, 4, 5, 7, 86, 126, 131, 206, 207, 311, 1123, 1213, 2113, 4111, 10921, 12211, 16581, 21121, 21211, 22111, 39660, 51558, 52940, 60812, 61504, 63548, 68822, 81303, 83409, 87081, 87451, 89708, 94523, 97307, 106118, 108527, 110387, 111611, 120831, 160271

Offset: 1

Author

Jaroslav Krizek, Oct 05 2016

Keywords

• nonn
• base

Comments

Numbers k such that A067342(k) = A277216(k).

Prime terms: 2, 3, 5, 7, 131, 311, 1123, 1213, 2113, 4111, 12211, ...

Corresponding values of sigma(a(n)): 1, 3, 4, 7, 6, 8, 132, 312, 132, 312, 312, 312, 1124, 1214, 2114, ...

Only 196 terms less than 35*10^8. - Robert G. Wilson v, Oct 07 2016

Alternatively, numbers k such that sigma(k) is in A034710. - Charlie Neder, Dec 27 2018

Examples

			86 is a term because sigma(86) = 132; sum and product of digits of 132 = 6.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..196 (first 100 terms from Jaroslav Krizek)

Crossrefs

Cf. A000203, A007953, A007954, A034710.

Cf. A067342 (sum of decimal digits of sigma(n)), A277216 (product of decimal digits of sigma(n)).

Programs

Magma

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

Mathematica

Select[Range@ 200000, Total@ # == Times @@ # &@ IntegerDigits@ DivisorSigma[1, #] &] (* Michael De Vlieger, Oct 06 2016 *)

PARI

isok(n) = my(d=digits(sigma(n))); vecprod(d) == vecsum(d); \\ Michel Marcus, Mar 02 2019