A355929 -id:A355929 - cp's OEIS frontend

A069070 Numbers n such that n*sigma(n) is a perfect square.

1, 40, 81, 135, 216, 224, 400, 819, 1372, 3240, 3744, 4650, 6318, 18144, 21700, 27930, 30240, 32400, 32760, 69312, 71148, 91694, 111132, 174592, 175500, 185220, 215472, 241395, 278318, 293907, 327600, 336675, 362700, 386232, 515450, 958737

Offset: 1

Benoit Cloitre, Apr 05 2002

Also n such that the squarefree part of n (A007913) equals the squarefree part of sigma(n), A355928.
Also n such that abundancy of n, sigma(n)/n is a rational square. - Michel Marcus, Oct 06 2013
See A230043, resp. A230538, for n whose abundancy is a rational cube, resp. fourth power. - M. F. Hasler, Nov 02 2013

Giovanni Resta, Table of n, a(n) for n = 1..1896 (terms < 4*10^12, first 500 terms from Donovan Johnson)

Cf. A000203, A000290, A007913, A064987, A355928.
Cf. A008848, A027687 (subsequences).
Cf. also A230043, A230538.
Positions of 0's in A355929.

Select[Range[1000000],IntegerQ[Sqrt[# DivisorSigma[1,#]]]&] (* Harvey P. Dale, Dec 24 2012 *)

for(n=1,1000000,if(issquare(n*sigma(n)),print1(n,",")))

isok(n) = issquare(sigma(n)/n); \\ Michel Marcus, Oct 06 2013

More terms from Rick L. Shepherd, Apr 07 2002

A355928 Squarefree part of the sum of divisors of n.

Original entry on oeis.org

1, 3, 1, 7, 6, 3, 2, 15, 13, 2, 3, 7, 14, 6, 6, 31, 2, 39, 5, 42, 2, 1, 6, 15, 31, 42, 10, 14, 30, 2, 2, 7, 3, 6, 3, 91, 38, 15, 14, 10, 42, 6, 11, 21, 78, 2, 3, 31, 57, 93, 2, 2, 6, 30, 2, 30, 5, 10, 15, 42, 62, 6, 26, 127, 21, 1, 17, 14, 6, 1, 2, 195, 74, 114, 31, 35, 6, 42, 5, 186, 1, 14, 21, 14, 3, 33, 30, 5, 10

Offset: 1

Antti Karttunen, Jul 24 2022

nonn

Not multiplicative.

Antti Karttunen, Table of n, a(n) for n = 1..20000
Index entries for sequences related to sigma(n)

Cf. A000203, A007913, A006532 (positions of 1's), A355929.

Cf. also A080398.

PARI
```
A355928(n) = core(sigma(n));
```

from sympy.ntheory.factor_ import core, divisor_sigma
def A355928(n): return core(divisor_sigma(n)) # Chai Wah Wu, Jul 28 2022

a(n) = A007913(A000203(n)).

a(n) = A355929(n) + A007913(n).

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A069070 Numbers n such that n*sigma(n) is a perfect square.

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A355928 Squarefree part of the sum of divisors of n.

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