

A167485


Smallest positive integer m such that n can be expressed as the sum of an initial subsequence of the divisors of m, or 0 if no such m exists.


2



1, 1, 0, 2, 3, 0, 5, 4, 7, 15, 12, 21, 6, 9, 13, 8, 12, 30, 10, 42, 19, 18, 20, 57, 14, 36, 46, 30, 12, 102, 29, 16, 21, 42, 62, 84, 22, 36, 37, 18, 27, 63, 20, 50, 43, 66, 52, 129, 33, 75, 40, 78, 48, 220, 34, 36, 28, 49, 60, 265, 24, 132, 61, 32, 56, 117, 54, 100, 67, 90, 84
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OFFSET

0,4


COMMENTS

It appears that 2 and 5 are the only zeros in this sequence. This would follow from a slightly stronger version of the Goldbach conjecture: every even integer > 22 can be expressed as the sum of two primes p and q, with 5 < p < q < 5p. Then odd numbers can be obtained for pq and even numbers for 5pq.
Is a(n) = o(n)?  Arkadiusz Wesolowski, Nov 09 2013


LINKS

Michel Marcus, Table of n, a(n) for n = 0..1000


EXAMPLE

The divisors of 15 are 1,3,5,15, with cumulative sums 1,4,9,24. Since this is the smallest number where 9 occurs in the sums, a(9) = 15.


PROG

(PARI) {u=vector(100); for(n=1, 1000, ds=divisors(n); s=0; for(k=1, #ds, s+=ds[k]; if(s>#u, break); if(!u[s], u[s]=n))); u}


CROSSREFS

Cf. A000203, A001065, A078587, A051444.
Sequence in context: A299762 A057637 A258913 * A294141 A265513 A140508
Adjacent sequences: A167482 A167483 A167484 * A167486 A167487 A167488


KEYWORD

nonn


AUTHOR

Franklin T. AdamsWatters, Nov 04 2009


STATUS

approved



