A077374 Odd numbers whose abundance b satisfies -10 <= b <= 10, where the abundance of a number n is A(n) = sigma(n) - 2n.

1, 3, 5, 7, 9, 11, 15, 21, 315, 1155, 8925, 32445, 442365, 815634435

Offset

1,2

Comments

Apart from {1, 3, 5, 7, 9, 11, 15, 21, 315}, subset of A088012. Probably finite. - Charles R Greathouse IV, Mar 28 2011

a(15) > 10^13. - Giovanni Resta, Mar 29 2013

The abundance of the given terms a(1..14) is: (-1, -2, -4, -6, -5, -10, -6, -10, -6, -6, 6, 6, 6, -6). See also A171929, A188263 and A188597 for numbers with abundancy sigma(n)/n close to 2. - M. F. Hasler, Feb 21 2017

a(15) > 10^22. - Wenjie Fang, Jul 13 2017

Links

Table of n, a(n) for n=1..14.

Eric Weisstein's World of Mathematics, Abundance

Example

sigma(32445) = 64896 and 32445*2 = 64890, which makes the odd number 32445 six away from perfection: A(32445) = 6 and hence in this sequence.

Mathematica

Select[Range[1, 10^6, 2], -10 <= DivisorSigma[1, #] - 2 # <= 10 &] (* Michael De Vlieger, Feb 22 2017 *)

Prog

(PARI) forstep(n=1, 442365, 2, if(abs(sigma(n)-2*n)<=10, print1(n, ", ")))

Crossrefs

Cf. A033879, A033880, A000203, A088012.

Sequence in context: A201646 A201647 A201648 * A133848 A220077 A201649

Adjacent sequences: A077371 A077372 A077373 * A077375 A077376 A077377

Keyword

nonn

Author

Jason Earls, Nov 30 2002

Extensions

815634435 from Farideh Firoozbakht, Jan 12 2004

Status

approved