A048251 -id:A048251 - cp's OEIS frontend

A048256 Numbers whose sum of divisors is 6^6 = 46656.

17490, 19410, 22578, 24610, 24910, 25466, 25910, 26554, 26818, 27285, 29342, 29733, 29762, 31102, 31535, 32043, 32997, 33985, 35585, 36635, 37985, 39697, 41393, 41837, 42347, 44047, 45637, 45739, 45937, 46117

Offset: 1

Labos Elemer

Sequence has A048253(6)=30 terms from A048251(6)=17490 to A048252(6)=46117. - Ray Chandler, Sep 01 2010

			The divisors of 19410 are 1, 2, 3, 5, 6, 10, 15, 30, 647, 1294, 1941, 3235, 3882, 6470, 9705, and 19410; their sum is 46656, so 19410 is in the sequence.

Cf. A006532, A020477, A019422, A019423, A018427, A048251-A048255.

Select[Range[6^6], DivisorSigma[1, # ] == 6^6 &] (* Ray Chandler, Sep 01 2010 *)

A048257 Integers whose sum of divisors is a 7th power.

Original entry on oeis.org

1, 93, 127, 11811, 112890, 120054, 124338, 127330, 132770, 133998, 134090, 137058, 138754, 139962, 146710, 148665, 148810, 149534, 153986, 155510, 160215, 161194, 164985, 167134, 170986, 173098, 183687, 184682, 187143, 191913, 198485, 206823, 206965, 207687

Offset: 1

Labos Elemer

nonn

If m and n are coprime members of the sequence, then m*n is also a member. - Robert Israel, May 10 2018

			Divisors(11811) = {1,3,31,93,127,381,3937,11811} and sigma(11811) = 16384 = 4^7.

Donovan Johnson, Table of n, a(n) for n = 1..1000
Frits Beukers, Florian Luca and Frans Oort, Power Values of Divisor Sums, The American Mathematical Monthly, Vol. 119, No. 5 (May 2012), pp. 373-380.

Cf. A000203, A006532, A020477, A019422, A019423, A019424, A048251-A048256, A048258.

filter:= n -> type(map(t -> t[2]/7, ifactors(numtheory:-sigma(n))[2]),list(integer)):
select(filter, [$1..21*10^4]); # Robert Israel, May 09 2018

Select[Range[210000],IntegerQ[Surd[DivisorSigma[1,#],7]]&] (* Harvey P. Dale, Jun 09 2017 *)

isok(n) = ispower(sigma(n), 7); \\ Michel Marcus, Dec 20 2013

sigma(a(n)) = x^7, where the initial values of x are 1, 2, 4, 6 (48 times), ...

A048258 Integers whose sum of divisors is an 8th power.

Original entry on oeis.org

1, 217, 57337, 600270, 621690, 669990, 685290, 693294, 693770, 699810, 725934, 747670, 769930, 774894, 782598, 805970, 813378, 823938, 835670, 839802, 854930, 865490, 873334, 895594, 918435, 920414, 923410, 931634, 935715, 959565, 965174, 969034, 969206

Offset: 1

Labos Elemer

nonn

			Divisors(217) = {1,7,31,217}, sum = 256 = 2^8.
Divisors(57337) = {1,7,8191,57337}, sum = 65536 = 4^8.
Divisors(1676377) = {1,647,2591,1676377}, sum = 1679616 = 6^8.

Donovan Johnson, Table of n, a(n) for n = 1..1000
Frits Beukers, Florian Luca and Frans Oort, Power Values of Divisor Sums, The American Mathematical Monthly, Vol. 119, No. 5 (May 2012), pp. 373-380.

Cf. A006532, A020477, A019422, A019423, A019424, A048251-A048257.

Select[Range[10^6], IntegerQ@ Surd[DivisorSigma[1, #], 8] &] (* Michael De Vlieger, Aug 01 2017, after Harvey P. Dale at A048257 *)

isok(n) = ispower(sigma(n), 8); \\ Michel Marcus, Dec 30 2013

Sigma(1, a(n)) = x^8, where the initial values of x are 1, 2, 4, 6 (occurs 85 times), ...

A180265 a(n) = smallest k such that sigma(k) = 14^n, or zero if no such k exists.

Original entry on oeis.org

1, 13, 0, 1164, 15132, 230484, 2823492, 36705396, 508541124, 7194470556, 100696385244, 1503091145388, 19540184890044, 273550891167372, 3811871194625676, 53378900339114532, 727176010568075796, 10177815744800162004, 142523339476298463228, 1994910930816765350844, 27918212600229725023068

Offset: 0

Walter Kehowski, Aug 22 2010

nonn

			a(0)=1 since sigma(1)=14^0=1. a(1)=13 since sigma(13)=14. a(2)=0 since no N exists such that sigma(N)=14^2. a(6)=2823492=2^2*3*7*33613 since sigma(2823492)=14^6 is the first 6th power. a(7)=36705396=2^2*3*7*13*33613 since sigma(36705396)=14^7 is the first 7th power.

Max Alekseyev, Table of n, a(n) for n = 0..100

Cf. A046528, A048251, A110077, A180460, A180461, A180462, A180463, A180464

Edited (including b-file) by N. J. A. Sloane, Oct 05 2010

Terms a(25) onward from Max Alekseyev, Mar 04 2014

A180460 a(n) is the smallest number m such that sigma(m)=22^n, or 0 if m does not exist.

Original entry on oeis.org

1, 0, 0, 10363, 136647, 3018141, 66411009, 1636922343, 31276995183, 688217286267, 15200749439001, 324029599659171, 7264291502741679, 160447401116572437, 3530475812620849113, 75514126111770824037, 1662716417771040164631, 36586320846189859358019, 804905851136700392012493, 17704604426749226872106319

Offset: 0

Walter Kehowski, Sep 06 2010

nonn

Conjecture: Given any even integer E not a power of 2 (see A078426) there exists a positive integer N such that for all n>=N the equation sigma(m)=E^n has at least one solution for m.

			a(4)=136647=3^4*7*241 since sigma(3^4*7*241)=(11^2)(2^3)(2*11^2)=2^4*11^4 and 136647 is the smallest such number.

Max Alekseyev, Table of n, a(n) for n = 0..100

Cf. A048251, A110077, A180265, A180461, A180462, A180463, A180464.

Terms a(37) onward (in b-file) from Max Alekseyev, Mar 04 2014

A180461 a(n) is the smallest number m such that sigma(m)=26^n, or 0 if m does not exist.

Original entry on oeis.org

1, 0, 0, 0, 312399, 8911029, 187131609, 5560483959, 126501010209, 3186244194273, 85514682943809, 2206011586559697, 55462952723504823, 1577373555132452973, 37744962467192492463, 974816528291192900817, 25345238283868264629273, 658976194648474007782617, 17245346702665551116114601

Offset: 0

Walter Kehowski, Sep 06 2010

nonn

			a(4)=312399=3^2*103*337 since sigma(3^2*103*337)=(13)*(2^3*13)*(2*13^2)=2^4*13^4 and 312399 is the smallest such number.

Max Alekseyev, Table of n, a(n) for n = 0..100

Cf. A048251, A110077, A180265, A180460, A180462, A180463, A180464.

Terms a(17) onward from Max Alekseyev, Mar 04 2014

A180462 a(n) is the smallest number m such that sigma(m)=34^n, or 0 if m does not exist.

Original entry on oeis.org

1, 0, 0, 38659, 1333447, 45356239, 1542131167, 52432478719, 0, 44114690056791, 1545604624685757, 52550557239372861, 1542390446782691499, 52463299805385993363, 1783774217997898256739, 60648345436543315211523, 2091915317967934350057159, 69957029735592536691912261

Offset: 0

Walter Kehowski, Sep 06 2010

nonn

			a(3)=38659=67*577 since sigma(67*577)=(2^2*17)*(2*17^2)=2^3*17^3 and 38659 is the smallest such number.

Max Alekseyev, Table of n, a(n) for n = 0..100

Cf. A048251, A110077, A180265, A180460, A180461, A180463, A180464.

Terms a(16) onward from Max Alekseyev, Mar 04 2014

A180463 a(n) is the smallest number m such that sigma(m)=38^n, or 0 if m does not exist.

Original entry on oeis.org

1, 37, 0, 0, 0, 0, 0, 85811686941, 3175032416817, 159809964979789, 4561513295803851, 155532888827892597, 5754716886632026089, 249887680992407652771, 8319571903089894983277, 307824160414326114381249, 12077787753685017948512649, 455818072892233197941369463

Offset: 0

Walter Kehowski, Sep 06 2010

nonn

			a(7)=85811686941=3*28603895647 since sigma(85811686941)= (2^2)*(2^5*19^7)=2^7*19^7 and 85811686941 is the smallest such number.

Max Alekseyev, Table of n, a(n) for n = 0..100

Cf. A048251, A110077, A180265, A180460, A180461, A180462, A180464.

Terms a(16) onward from Max Alekseyev, Mar 03 2014

A180464 a(n) is the smallest number m such that sigma(m)=46^n, or 0 if m does not exist.

Original entry on oeis.org

1, 0, 0, 0, 0, 180217597, 6217507317, 325975026477, 15034820907837, 919684211139697, 31808042757482763, 1463508270300620883, 58746435953696315769, 2709539295335742607689, 138000408890542031957601, 5718143312090439006662949, 263735727094699893912217269

Offset: 0

Walter Kehowski, Sep 06 2010

nonn

			a(5)=180217597=7*25745371 and sigma(180217597)=(2^3)*(2^2*23^5)=2^5*23^5 and 180217597 is the smallest such number.

Max Alekseyev, Table of n, a(n) for n = 0..100

Cf. A048251, A110077, A180265, A180460, A180461, A180462, A180463.

Terms a(15) onward from Max Alekseyev, Mar 03 2014

A048252 Largest number whose sum of divisors is 6^n.

Original entry on oeis.org

1, 5, 22, 187, 1219, 7597, 46117, 278857, 1676377, 10067797, 60450517, 362758177, 2176626817, 13060193977, 78363525817, 470183516857, 2820894903487, 16926601754197, 101559860054047, 609359671998037, 3656158318966357

Offset: 0

Labos Elemer

nonn

Terms of this sequence are products of distinct terms in A005105. - Ray Chandler, Sep 01 2010

Ray Chandler, Table of n, a(n) for n = 0..1000

Cf. A006532, A020477, A019422, A019423, A018427, A048251-A048256.

a(n) = {sn = 6^n; forstep(x=sn, 1, -1, if (sigma(x) == sn, return (x)););} \\ Michel Marcus, Dec 15 2013

a(9)-a(14) from Donovan Johnson, Sep 02 2008
a(15)-a(20) from Donovan Johnson, Nov 22 2008
Edited and extended by Ray Chandler, Sep 01 2010

cp's OEIS Frontend

A048256 Numbers whose sum of divisors is 6^6 = 46656.

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A048257 Integers whose sum of divisors is a 7th power.

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A048258 Integers whose sum of divisors is an 8th power.

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A180265 a(n) = smallest k such that sigma(k) = 14^n, or zero if no such k exists.

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A180460 a(n) is the smallest number m such that sigma(m)=22^n, or 0 if m does not exist.

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A180461 a(n) is the smallest number m such that sigma(m)=26^n, or 0 if m does not exist.

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A180462 a(n) is the smallest number m such that sigma(m)=34^n, or 0 if m does not exist.

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A180463 a(n) is the smallest number m such that sigma(m)=38^n, or 0 if m does not exist.

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A180464 a(n) is the smallest number m such that sigma(m)=46^n, or 0 if m does not exist.

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