A125747 -id:A125747 - cp's OEIS frontend

A117553 When adding some positive divisors of n in order from lowest divisor to highest divisor, a(n) is lowest sum achievable which is >= n.

1, 3, 4, 7, 6, 6, 8, 15, 13, 18, 12, 16, 14, 24, 24, 31, 18, 21, 20, 22, 32, 36, 24, 24, 31, 42, 40, 28, 30, 42, 32, 63, 48, 54, 48, 37, 38, 60, 56, 50, 42, 54, 44, 84, 78, 72, 48, 52, 57, 93, 72, 98, 54, 66, 72, 64, 80, 90, 60, 78, 62, 96, 104, 127, 84, 78, 68, 126, 96, 74, 72

Offset: 1

Leroy Quet, Mar 28 2006

nonn

Often, but not always, a(n)=n+A054024(n). The exceptions to this rule are at n=24, 36, 48, 60, 72, 84,90, 96, 108, ... - R. J. Mathar, Mar 14 2007

			12's divisors are 1,2,3,4,6 and 12. Adding the divisors in order we have:
1 = 1, 1+2 = 3, 1+2+3 = 6, 1+2+3+4 = 10, 1+2+3+4+6 = 16 and 1+2+3+4+6+12 = 28.
Of these sums, 1+2+3+4+6 = 16 is the lowest which is >= 12. So a(12) = 16.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A117552, A125746, A125747.

A117553 := proc(n) local divs,a,i ; divs := numtheory[divisors](n) ; a := op(1,divs) ; i := 1 ; while a < n do i := i+1 ; a := a+op(i,divs) ; od ; RETURN(a) ; end: for n from 1 to 80 do printf("%d, ",A117553(n)) ; od ; # R. J. Mathar, Mar 14 2007

Table[Select[Accumulate[Divisors[n]],#>=n&,1],{n,80}]//Flatten (* Harvey P. Dale, Apr 05 2017 *)

More terms from R. J. Mathar, Mar 14 2007

A125746 a(n) = smallest divisor d of n such that n <= {sum of d and all smaller divisors of n}.

Original entry on oeis.org

1, 2, 3, 4, 5, 3, 7, 8, 9, 10, 11, 6, 13, 14, 15, 16, 17, 9, 19, 10, 21, 22, 23, 8, 25, 26, 27, 14, 29, 15, 31, 32, 33, 34, 35, 12, 37, 38, 39, 20, 41, 21, 43, 44, 45, 46, 47, 16, 49, 50, 51, 52, 53, 27, 55, 28, 57, 58, 59, 20, 61, 62, 63, 64, 65, 33, 67, 68, 69, 35, 71, 24, 73

Offset: 1

Leroy Quet, Dec 05 2006

nonn

Original name of this sequence: a(n) is the smallest positive integer such that (sum{k|n, 1<=k<=a(n)} k) is >= n.

			The divisors of 12 are 1,2,3,4,6,12. 1+2+3+4 = 10, which is smaller than 12; but 1+2+3+4+6 = 16, which is >= 12. So a(12) = 6.

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A125747, A117553, A300826 (= n/a(n)).

f[n_] := Block[{k = 1, d = Divisors[n]},While[Sum[d[[i]], {i, k}] < n, k++ ];d[[k]]];Table[f[n], {n, 76}] (* Ray Chandler, Dec 06 2006 *)

A125746(n) = { my(k=0,s=0); fordiv(n,d, k++; s += d; if(s>=n,return(d))); }; \\ Antti Karttunen, Mar 21 2018

Extended by Ray Chandler, Dec 06 2006

Name changed by Antti Karttunen, Mar 21 2018

A302110 Let d be the list of A000005(n) = tau(n) divisors of n. Then a(n) is the largest k such that Sum_{i=1..#d-k} d_i > n.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1

Offset: 1

David A. Corneth, Apr 01 2018

Records (0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, ...) occur at 1, 6, 24, 120, 240, 720, 1260, 2520, 5040, 15120, 27720, 55440, ... - Antti Karttunen, Apr 02 2018

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A000005, A023196, A125746, A125747, A300826.

A125747(n) = { my(k=0,s=0); fordiv(n,d, k++; s += d; if(s>=n,return(k))); };
A302110(n) = (numdiv(n) - A125747(n)); \\ Antti Karttunen, Apr 02 2018

a(n) = A000005(n) - A125747(n).

a(n) > 0 if and only if n is in A023196.

cp's OEIS Frontend

A117553 When adding some positive divisors of n in order from lowest divisor to highest divisor, a(n) is lowest sum achievable which is >= n.

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A125746 a(n) = smallest divisor d of n such that n <= {sum of d and all smaller divisors of n}.

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A302110 Let d be the list of A000005(n) = tau(n) divisors of n. Then a(n) is the largest k such that Sum_{i=1..#d-k} d_i > n.

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