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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. 0
120, 672, 4320, 4680, 26208, 523776, 20427264, 29795040, 34369920, 96445440, 197064960, 459818240, 557107200 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

3-perfect 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

Table of n, a(n) for n=1..13.

PROG

(PARI) isok(n) = {if (sigma(n) < 2*n, return (0)); my(d = divisors(n), s = 0); for (k=1, #d-1, 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 = #d-1, 1, -1, if(s <= 2*n, return(s == 2*n)); s-=d[i]); 0 \\ David A. Corneth, Feb 11 2019

CROSSREFS

Cf. A005820 (3-perfect numbers), A055153 (abundancy 7/2).

Cf. A064510, A194472 (both with equal to m rather than to 2*m).

Sequence in context: A179963 A229568 A292365 * A113546 A281771 A166069

Adjacent sequences:  A306370 A306371 A306372 * A306374 A306375 A306376

KEYWORD

nonn,more

AUTHOR

Michel Marcus, Feb 11 2019

EXTENSIONS

a(11)-a(13) from Jinyuan Wang, Feb 11 2019

STATUS

approved

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Last modified April 6 11:38 EDT 2020. Contains 333273 sequences. (Running on oeis4.)