

A306373


Integers m such that the sum of the first k divisors is equal to 2*m for some k less than the number of divisors of m.


1



120, 672, 4320, 4680, 26208, 523776, 20427264, 29795040, 34369920, 96445440, 197064960, 459818240, 557107200
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OFFSET

1,1


COMMENTS

3perfect numbers (A005820) are terms.
All known terms of A055153 (abundancy 7/2) are terms.
1907020800 (with abundancy 23/6) is a term too.
A055153 is a subsequence, because no term of that sequence may be odd and so for each k in A055153 we have 2*k = sigma(k)  k  k/2.  Charlie Neder, Feb 12 2019


LINKS



PROG

(PARI) isok(n) = {if (sigma(n) < 2*n, return (0)); my(d = divisors(n), s = 0); for (k=1, #d1, s += d[k]; if (s == 2*n, return (1)); if (s > 2*n, break); ); return (0); }
(PARI) is(n) = my(d = divisors(n), s = vecsum(d)  d[#d]); forstep(i = #d1, 1, 1, if(s <= 2*n, return(s == 2*n)); s=d[i]); 0 \\ David A. Corneth, Feb 11 2019


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



