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.

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

Offset: 1

Author

Michel Marcus, Feb 11 2019

Keywords

• nonn
• more

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

Crossrefs

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

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

Programs

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

Extensions

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