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

Author

Jud McCranie, Dec 11 1999

Keywords

• fini
• nonn
• full

Comments

a(1456) = 20161 is the last term.

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

Examples

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

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.

Crossrefs

Complement of A048260.

Cf. A005101.

Programs

PARI

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