A048242 Numbers that are not the sum of two abundant numbers (not necessarily distinct).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 33, 34, 35, 37, 39, 41, 43, 45, 46, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109

Offset

1,2

Comments

a(1456) = 20161 is the last term.

a(38) = 46 is the largest even term. - Alonso del Arte, Sep 11 2016

References

Problem 13, ABACUS.

Thomas R. Parkin and Leon J. Lander, Abundant numbers, Aerospace Corporation, Los Angeles, 1964, 119 unnumbered pages. Copy deposited in UMT file.

Joe Roberts, Lure of the Integers, MAA Spectrum, 1992, p. 273, integer 20161.

David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Book, 1986, p. 175, entry 20161.

Links

T. D. Noe, Table of n, a(n) for n = 1..1456 (complete sequence)

F. A. E. Pirani, Problems For Solution "E903", The American Mathematical Monthly, Vol. 57, No. 2, (February 1950), p. 113.

F. A. E. Pirani, Leo Moser and John Selfridge, E903, The American Mathematical Monthly, Vol. 57, No. 8. (October 1950), pp. 561-562.

Project Euler, Non-abundant sums Problem 23

Review of Abundant Numbers by Thomas R. Parkin and Leon J. Lander, Mathematics of Computation, Vol. 19, No. 90. (April 1965), p. 334.

Example

12 is abundant, so 24=12+12 is not a term.

Prog

(PARI) setminus([1..20161], setbinop((x, y)->x+y, select(k->sigma(k, -1)>2, [1..16695]))) \\ Charles R Greathouse IV, Oct 10 2017

Crossrefs

Complement of A048260.

Cf. A005101.

Sequence in context: A364354 A289555 A354808 * A272076 A335280 A335282

Adjacent sequences: A048239 A048240 A048241 * A048243 A048244 A048245

Keyword

fini,nonn,full

Author

Jud McCranie, Dec 11 1999

Status

approved