A232566 Let x(0)x(1)x(2)... x(q) denote the decimal expansion of n and sopf(n) the sum of the distinct prime divisors of n. Sequence lists the numbers n such that x(0)/sopf(n) + x(1)/sopf(n) + ... + x(q)/sopf(n) + x(0)*x(1)*x(2)*...*x(q)/sopf(n) is an integer.

2, 3, 4, 5, 7, 8, 9, 12, 14, 19, 29, 34, 49, 59, 64, 66, 74, 79, 89, 94, 117, 135, 144, 147, 155, 160, 175, 189, 192, 243, 250, 319, 375, 391, 448, 486, 512, 545, 627, 648, 657, 729, 735, 756, 784, 792, 825, 864, 875, 936, 968, 975, 1144, 1232, 1239, 1344, 1408

Offset

1,1

Comments

The corresponding integers are 2, 2, 4, 2, 2, 8, 6, 1, 1, 1, 1, 1, 7, 1, 17, 3, 1, 1, 1, 1, 1, 3, 5, 4, 1, 1, 4, 9, 6, 11,...

The primes of this sequence are 2, 3, 5, 7, 19, 29, 59, 79, 89. It seems that this subsequence is probably finite (no further terms less than 10^7).

Links

Table of n, a(n) for n=1..57.

Example

657 is in the sequence because the prime divisors of 657 are 3 and 73 => sopf(657) = 3+73 = 76 and 6/76 + 5/76 + 7/76 + 6*5*7/76 = 3 is an integer.

Maple

with(numtheory):for n from 2 to 1500 do:x:=convert(n, base, 10):n1:=nops(x):y:=factorset(n):n2:=nops(y):p:=1:s:=0:for i from 1 to n2 do:s:=s+y[i]:od:s1:=0:for j from 1 to n1 do:s1:=s1+x[j]/s:p:=p*x[j]:od:s1:=s1+p/s:if s1=floor(s1) then printf(`%d, `, n):else fi:od:

Crossrefs

Cf. A008472.

Sequence in context: A051204 A335154 A278181 * A192649 A102363 A201816

Adjacent sequences: A232563 A232564 A232565 * A232567 A232568 A232569

Keyword

nonn,base

Author

Michel Lagneau, Nov 26 2013

Status

approved