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

1,1

Comments

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

Links

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

Example

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

Prog

(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

Crossrefs

Cf. A007913, A035316, A225880, A225881.

Sequence in context: A345286 A338485 A344334 * A281768 A225892 A366933

Adjacent sequences: A225879 A225880 A225881 * A225883 A225884 A225885

Keyword

nonn

Author

Antonio Roldán, May 19 2013

Status

approved