A132783 Numbers n with the property that the difference between the two largest proper divisors of n equals the sum of proper divisors of the digit sum of n.

57, 5767, 6497, 7387, 29177, 30967, 35657, 37627, 52891, 53297, 61937, 70747, 75067, 96091, 114857, 118961, 126727, 145097, 190087, 194417, 215287, 221777, 244961, 307961, 335177, 348091, 370817, 408257, 414727, 423737, 462391, 585161

Offset

1,1

Comments

All but two members of the sequence below 20000000 are the products of two primes separated by 6 or 16 and have digit sums of 25 or 26, which have proper divisor sums of 6 (=1+5) and 16(=1+2+13) respectively. The exceptions are the 1st term (57), which has a digit sum of 12 and the 67th (18999857), which has a digit sum of 56.

Links

Table of n, a(n) for n=1..32.

Example

The divisors of 57 are 1, 3 and 19, so the difference of the two largest is 16.
The divisors of its digit sum (12=5+7) are 1,2,3,4 and 6, which also sum to 16.

Mathematica

ok[n_] := Block[{d = Divisors@n, s = Total@ IntegerDigits@ n}, Length[d] > 2 && d[[-2]] - d[[-3]] == DivisorSigma[1, s] - s]; Select[Range[10^5], ok] (* Giovanni Resta, Jun 09 2015 *)

Prog

A program to test an individual integer, written in APL, is available if required.

Crossrefs

Sequence in context: A281567 A012165 A209512 * A221445 A218353 A127455

Adjacent sequences: A132780 A132781 A132782 * A132784 A132785 A132786

Keyword

nonn,base

Author

Paul H. Smith (decisionbydesign(AT)aol.com), Nov 17 2007

Status

approved