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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. 1
 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: A229568 A342923 A292365 * A356548 A113546 A281771 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 July 17 12:34 EDT 2024. Contains 374377 sequences. (Running on oeis4.)