A081532 -id:A081532 - cp's OEIS frontend

A081533 Sum of terms in row n of A081532.

1, 3, 7, 12, 31, 28, 127, 60, 91, 124, 2047, 168, 8191, 508, 403, 360, 131071, 546, 524287, 744, 1651, 8188, 8388607, 1170, 3751, 32764, 2821, 3048, 536870911, 2418, 2147483647, 2880, 26611, 524284, 15367, 4368, 137438953471, 2097148, 106483

Offset: 1

Amarnath Murthy, Mar 28 2003

nonn

Cf. A005179, A081532.

a(n) = sigma(A005179(n)).

More terms from David Wasserman, Jun 07 2004

A119265 Triangle read by rows, 1<=k<=n: T(n,k) = k-th divisor of the smallest odd number with exactly n divisors, A038547.

Original entry on oeis.org

1, 1, 3, 1, 3, 9, 1, 3, 5, 15, 1, 3, 9, 27, 81, 1, 3, 5, 9, 15, 45, 1, 3, 9, 27, 81, 243, 729, 1, 3, 5, 7, 15, 21, 35, 105, 1, 3, 5, 9, 15, 25, 45, 75, 225, 1, 3, 5, 9, 15, 27, 45, 81, 135, 405, 1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105

Offset: 1

Reinhard Zumkeller, May 11 2006

Jean-François Alcover, Table of n, a(n) for n = 1..5050

Cf. A081532, A000005, A005408.

A038547 = Cases[Import["https://oeis.org/A038547/b038547.txt", "Table"], {, }][[All, 2]];
row[n_] := row[n] = Divisors[A038547[[n]]];
T[n_, k_] := row[n][[k]];
Table[T[n, k], {n, 1, 100}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 19 2021 *)

T(n,1) = 1; T(n,n) = A038547(n);

T(n,k) = A027750(A006218(A038547(n)-1) + k).

A171783 Third smallest divisor of smallest number having exactly n divisors.

Original entry on oeis.org

4, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4

Offset: 3

J. Lowell, Oct 12 2010

nonn

Conjecture: a(n) = 4 for all prime numbers >= 3 and 3 for all composites

Third column of triangle in A081532. - N. J. A. Sloane, Oct 12 2010.

			a(4) = 3 because the divisors of 6 are 1, 2, 3, 6.

Antti Karttunen, Table of n, a(n) for n = 3..2000 (computed from the b-file of A005179 provided by _Don Reble_)

Cf. A081532, A171784. - N. J. A. Sloane, Oct 12 2010.

Cf. A005179, A292269.

a(n) = A292269(A005179(n)) for n >= 3. - Antti Karttunen, Oct 04 2017

More terms from R. J. Mathar, Oct 13 2010

A085683 a(n) = Sum_{k = 1..N-1} floor(N/k) where N is the n-th prime.

Original entry on oeis.org

2, 4, 9, 15, 28, 36, 51, 59, 75, 102, 112, 141, 159, 169, 187, 218, 248, 262, 293, 313, 327, 357, 378, 412, 460, 483, 493, 515, 529, 553, 636, 658, 696, 706, 767, 781, 821, 857, 877, 918, 952, 972, 1032, 1048, 1071, 1085, 1167, 1239, 1266, 1280, 1306, 1342, 1364, 1422

Offset: 1

N. J. A. Sloane, Oct 28 2008

nonn

The old entry with this sequence number was a duplicate of A081532.

Giovanni Resta, Table of n, a(n) for n = 1..10000
R. K. Guy, Conway's prime producing machine, Math. Mag. 56 (1983), no. 1, 26-33 (see p. 33).

Cf. A006218, A077597.

(Rest@ FoldList[ Plus, 0, DivisorSigma[0, Range@ Prime@ 100]])[[ Prime@ Range@ 100]] -1 (* Giovanni Resta, Jun 09 2015 *)

from math import isqrt
from sympy import prime
def A085683(n): return -(s:=isqrt(m:=prime(n)))**2+(sum(m//k for k in range(1,s+1))<<1)-1 # Chai Wah Wu, Oct 23 2023

A171784 Fourth smallest divisor of smallest number having exactly n divisors.

Original entry on oeis.org

6, 8, 4, 8, 4, 4, 4, 8, 4, 8, 4, 4, 4, 8, 4, 8, 4, 4, 4, 8, 4, 4, 4, 4, 4, 8, 4, 8, 4, 4, 4, 4, 4, 8, 4, 4, 4, 8, 4, 8, 4, 4, 4, 8, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 8, 4, 8, 4, 4, 4, 4, 4, 8, 4, 4, 4, 8, 4, 8, 4, 4, 4, 4, 4, 8, 4, 4, 4, 8, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 4, 4, 8, 4, 4, 4, 8, 4, 8, 4, 4, 4, 8, 4

Offset: 4

J. Lowell, Oct 12 2010

nonn

Fourth column of triangle in A081532. - N. J. A. Sloane, Oct 12 2010.

			a(5) = 8 because divisors of 16 are 1,2,4,8,16.

David A. Corneth, Table of n, a(n) for n = 4..10003 (first 1997 terms from Antti Karttunen)

Cf. A005179, A081532, A171783.

More terms from R. J. Mathar, Oct 13 2010

cp's OEIS Frontend

A081533 Sum of terms in row n of A081532.

Views

Author

Keywords

Crossrefs

Formula

Extensions

A119265 Triangle read by rows, 1<=k<=n: T(n,k) = k-th divisor of the smallest odd number with exactly n divisors, A038547.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A171783 Third smallest divisor of smallest number having exactly n divisors.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

Extensions

A085683 a(n) = Sum_{k = 1..N-1} floor(N/k) where N is the n-th prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Python

A171784 Fourth smallest divisor of smallest number having exactly n divisors.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions