A225881 -id:A225881 - cp's OEIS frontend

A225882 Numbers k such that core(k) is equal to the sum of the proper square divisors of k, where core(k) = A007913(k).

20, 90, 336, 650, 5440, 7371, 13000, 14762, 28730, 30240, 83810, 87296, 130682, 147420, 218400, 280370, 295240, 406875, 708122, 924482, 1397760, 1875530, 2613640, 3536000, 4881890, 4960032, 5884851, 7856640, 7893290, 8137500

Offset: 1

Antonio Roldán, May 19 2013

nonn

If p is prime and p^2 + 1 squarefree, then p^2*(p^2 + 1) is in the sequence.

			13000 is a term because core(13000) = 130 = 100 + 25 + 4 + 1.

Giovanni Resta, Table of n, a(n) for n = 1..282 (terms < 5*10^11; first 80 terms from Charles R Greathouse IV)

Cf. A007913, A035316, A225880, A225881.

for(n=2,10^8,if(core(n)==sumdiv(n,d,d*issquare(d)),print(n)))

ssd(f)=prod(i=1,#f[,1],(f[i,1]^(f[i,2]+2-f[i,2]%2)-1)/(f[i,1]^2-1))
is(n)=my(f=factor(n));prod(i=1,#f[,1],f[i,1]^(f[i,2]%2))==ssd(f) && n>1 \\ Charles R Greathouse IV, May 20 2013

A225880 Numbers that can be expressed as the product of largest odd proper divisor and the sum of odd proper divisors.

Original entry on oeis.org

12, 56, 672, 992, 11904, 16256, 55552, 195072, 666624, 910336, 10924032, 16125952, 67100672, 193511424, 805208064, 903053312, 3757637632, 10836639744, 17179738112, 45091651584, 66563866624, 206156857344, 274877382656, 798766399488, 962065334272, 1090788524032

Offset: 1

Antonio Roldán, May 19 2013

nonn

The numbers a(n) can be expressed as 2^(m+n+p+...)*(2^m-1)*(2^n-1)*(2^p-1)... with 2^m-1, 2^n-1, 2^p-1 distinct Mersenne primes (A000668(n)). Example: 55552 = 2^6*7*31=2^6*(2^3-1)*(2^5-1).
This sequence is supersequence of A139256.
The number a(n) is in A139256 or a(n) is product of twice even perfect numbers A139256(n). Example: 1090788524032 = 16256*67100672 = (2*8128)*(2*33550336) = A139256(4) * A139256(5).

			11904 = 93*(93+31+3+1).

Cf. A225882, A225881.

gdivodd(n)={m=n;while(m/2==m\2,m=m/2);return(m)}
{for (n=2,2*10^8,m=gdivodd(n)*sumdiv(n, d, d*(d%2));if(m==n,print(n)))}

cp's OEIS Frontend

A225882 Numbers k such that core(k) is equal to the sum of the proper square divisors of k, where core(k) = A007913(k).

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A225880 Numbers that can be expressed as the product of largest odd proper divisor and the sum of odd proper divisors.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI