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

Author

Antonio Roldán, May 19 2013

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A007913, A035316, A225880, A225881.

Programs

PARI

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

PARI

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