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A225882 Numbers n such that core(n) is equal to the sum of the proper square divisors of n, where core(n) = A007913(n). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Charles R Greathouse IV and 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: A220200 A242656 A264851 * A281768 A225892 A211140

Adjacent sequences:  A225879 A225880 A225881 * A225883 A225884 A225885

KEYWORD

nonn

AUTHOR

Antonio Roldán, May 19 2013

STATUS

approved

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Last modified July 25 04:48 EDT 2017. Contains 289779 sequences.