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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 26 11:06 EST 2020. Contains 331279 sequences. (Running on oeis4.)