A169981 -id:A169981 - cp's OEIS frontend

A175432 a(n) = the greatest number k such that sigma(n) = m^k for any m >= 1 (sigma = A000203).

1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 2, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 2, 1, 1, 1, 1, 1, 1

Offset: 1

Jaroslav Krizek, May 10 2010

nonn

a(A175431(n)) = 1 for n >= 1.
a(A065496(n)) > 1 for n >= 1.
It appears that the record values in this sequence, 1, 2, 3, 5, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, ..., is A180221 with a 1 prepended, at least through term #469. Is this a theorem? - Ray Chandler, Aug 20 2010

			For n = 7, a(7) = 3 because sigma(7) = 8 = 2^3.

Antti Karttunen, Table of n, a(n) for n = 1..16384

For locations of records see A169981.

Cf. A000203, A052409, A175433.

Array[Apply[GCD, FactorInteger[DivisorSigma[1, #]][[All, -1]]] &, 105] (* Michael De Vlieger, Nov 05 2017 *)

a(n)=max(ispower(sigma(n)),1) \\ Charles R Greathouse IV, Feb 14 2013

a(n) = A052409(A000203(n)). - N. J. A. Sloane, Aug 19 2010

a(n) = log_A175433(n) [A000203(n)].

A180162 a(n) is the smallest number N such that sigma(N) is an n-th power but not a higher power, with a(n) = 0 if no such number exists.

Original entry on oeis.org

1, 2, 3, 7, 510, 21, 17490, 93, 217, 381, 651, 118879530, 2667, 8191, 11811, 24573, 57337, 82677, 172011, 393213, 761763, 1572861, 2752491, 5332341, 11010027, 21845397, 48758691, 85327221, 199753347, 341310837, 677207307, 1398273429

Offset: 0

Walter Kehowski, Aug 14 2010, Aug 19 2010

nonn

			a(4)=510 since 510=2*3*5*17, sigma(510)=2^4*3^4.
a(11)=2*3*5*7*11*53*971=118879530 since sigma(118879530)=6^11.

Ray Chandler, Table of n, a(n) for n = 0..469

Cf. A065496, A000203, A175432, A169981.

with(numtheory);
egcd:=proc(n::posint) local L; if n>1 then L:=ifactors(n)[2]; L:=map(z-> z[2],L); igcd(op(L)) else 0 fi end:
P:={}: SP:={}:
for w to 1 do
for n from 1 to 12^6 do
sn:=sigma(n);
esn:=egcd(sn);
if not esn in P then
P:=P union {esn};
SP:=SP union {[esn,n]};
printf("n=%d, esn=%d, sn=...\n",n,esn);
print(ifactor(sn));
fi;
od; #n
od; #w
P; SP;

a(n) >= A063869(n). - R. J. Mathar, Aug 20 2010

a(11) found by Walter Kehowski and Artur Jasinski, Aug 16 2010
Edited by N. J. A. Sloane, Aug 19 2010
a(23) onwards from Ray Chandler, Aug 19 2010

cp's OEIS Frontend

A175432 a(n) = the greatest number k such that sigma(n) = m^k for any m >= 1 (sigma = A000203).

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