A237428 - OEIS

A237428

Numbers k with following property: List all proper divisors of k. Replace any composite number in the list with its proper divisors. Repeat. Sum of remaining numbers (1's and primes) is equal to k.

6, 126, 3808, 19360, 104320, 4317184, 126764640

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OFFSET

1,1

COMMENTS

Is there a largest term? Is there any odd term?

a(8) if it exists is greater than 10^9. - Giovanni Resta, Feb 07 2014

Numbers k such that k = A074206(k) + Sum_{p|k} (p-1)*A074206(k/p). - Charlie Neder, Jun 02 2019

LINKS

Table of n, a(n) for n=1..7.

EXAMPLE

6 is a term because: 1 + 2 + 3 = 6.

126 is a term because: [1 + 2 + 3 + (6 - 6) + 7 + (9 - 9) + (14 - 14) + (18 - 18) + (21 - 21) + (42 - 42) + (63 - 63)] + [1 + 2 + 3] + [1 + 3] + [1 + 2 + 7] + [1 + 2 + 3 + (6 - 6) + (9 - 9)] + [1 + 3 + 7] + [1 + 2 + 3 + (6 - 6) + 7 + (14 - 14) + (21 - 21)] + [1 + 3 + 7 + (9 - 9) + (21 - 21)] + [1 + 2 + 3] + [1 + 3] + [1 + 2 + 3] + [1 + 2 + 7] + [1 + 3 + 7] + [1 + 3] + [1 + 3 + 7] = 126.

MATHEMATICA

v[n_] := If[PrimeQ@n, 1, Block[{s = Sum[If[e == 1 || PrimeQ@e, e, v@e], {e, Most@ Divisors@n}]}, If[n < 1000, v[n] = s, s]]]; Select[Range@ 20000, # == v@# &] (* Giovanni Resta, Feb 07 2014 *)

CROSSREFS

Cf. A000203, A000396, A001065, A002033, A032741, A191150.

Sequence in context: A228290 A370715 A004993 * A255900 A133792 A081623

Adjacent sequences: A237425 A237426 A237427 * A237429 A237430 A237431

KEYWORD

more,nonn

AUTHOR

Lechoslaw Ratajczak, Feb 07 2014

EXTENSIONS

a(6)-a(7) from Giovanni Resta, Feb 07 2014

STATUS

approved