A234641 -id:A234641 - cp's OEIS frontend

A234638 Numbers n for which sigma(sigma(n)) is odd.

1, 3, 7, 10, 17, 21, 22, 30, 31, 46, 51, 52, 55, 66, 70, 71, 81, 93, 94, 97, 106, 115, 119, 127, 138, 154, 156, 165, 170, 199, 210, 213, 214, 217, 232, 235, 241, 253, 265, 282, 291, 298, 310, 318, 322, 337, 343, 345, 357, 364, 374, 381, 382, 385

Offset: 1

M. F. Hasler, Dec 28 2013

nonn

See A234641 for numbers n such that n^2 is in this sequence.

The primes in this sequence are 3 and A066436. - Robert Israel, Apr 05 2019

			3 is in the sequence because sigma(sigma(3)) = sigma(4) = 7, which is odd.
7 is in the sequence because sigma(sigma(7)) = sigma(8) = 15, which is odd.
8 is not in the sequence because sigma(sigma(8)) = sigma(15) = 24, which is even.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000203, A028982, A066436, A234641.

filter:= proc(n) uses numtheory; sigma(sigma(n))::odd end proc:
select(filter, [$1..1000]); # Robert Israel, Apr 05 2019

Select[Range[400], OddQ[DivisorSigma[1, DivisorSigma[1, #]]] &] (* Alonso del Arte, Dec 29 2013 *)

PARI
```
is(n)=bittest(sigma(sigma(n)),0)
```
PARI
```
for(n=1,999,is(n)&&print1(n","))
```

A234639 Numbers n for which sigma(sigma(sigma(n))) is odd.

Original entry on oeis.org

1, 2, 4, 16, 25, 29, 50, 64, 99, 100, 104, 116, 125, 137, 243, 279, 281, 309, 317, 343, 361, 373, 396, 408, 424, 440, 456, 461, 464, 486, 488, 500, 509, 519, 534, 538, 548, 558, 568, 585, 590, 603, 618, 632, 638, 641, 646, 686, 693, 703, 709, 718, 725, 746, 747, 783

Offset: 1

M. F. Hasler, Dec 28 2013

nonn

Also, numbers such that sigma(sigma(n)) is in A028982, i.e., a square or twice a square.

See A234640 for the subsequence of odd terms. See also A234638, and A234641 with further cross references.

R. J. Mathar, Table of n, a(n) for n = 1..404

n := 1 :
for k from 1 to 10000 do
    numtheory[sigma](k) ;
    numtheory[sigma](%) ;
    numtheory[sigma](%) ;
    if type(%,'odd') then
        printf("%d %d\n",n,k) ;
        n := n+1 ;
    end if;
end do: # R. J. Mathar, Oct 21 2014

sssoQ[n_]:=OddQ[Nest[DivisorSigma[1,#]&,n,3]]; Select[Range[800],sssoQ] (* Harvey P. Dale, Jul 06 2019 *)

for(n=1,999,sigma(sigma(sigma(n)))%2 && print1(n","))

A234640 Odd numbers n for which sigma(sigma(sigma(n))) is odd.

Original entry on oeis.org

1, 25, 29, 99, 125, 137, 243, 279, 281, 309, 317, 343, 361, 373, 461, 509, 519, 585, 603, 641, 693, 703, 709, 725, 747, 783, 807, 809, 875, 883, 895, 905, 929, 933, 979, 995, 1003, 1007, 1043, 1059, 1091, 1121, 1133, 1323, 1591, 1597, 1701, 1707, 1779, 1801, 1895, 1973

Offset: 1

M. F. Hasler, Dec 28 2013

nonn

Also, odd numbers such that sigma(sigma(n)) is in A028982.

Subsequence of odd terms of A234639. See also A234638, and A234641 with further cross references.

forstep(n=1,1999,2,sigma(sigma(sigma(n)))%2 && print1(n","))

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A234638 Numbers n for which sigma(sigma(n)) is odd.

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A234639 Numbers n for which sigma(sigma(sigma(n))) is odd.

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Author

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Comments

Links

Programs

Maple

Mathematica

PARI

A234640 Odd numbers n for which sigma(sigma(sigma(n))) is odd.

Views

Author

Keywords

Comments

Programs

PARI