A048260 -id:A048260 - cp's OEIS frontend

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

Jud McCranie, Dec 11 1999

a(1456) = 20161 is the last term.

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

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

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.

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.

Complement of A048260.

Cf. A005101.

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

A168226 Even numbers which are the sum of two odd abundant numbers.

Original entry on oeis.org

1890, 2520, 3150, 3780, 4410, 5040, 5670, 6300, 6720, 6930, 7350, 7380, 7560, 7770, 7980, 8010, 8190, 8370, 8400, 8610, 8640, 8820, 9000, 9030, 9240, 9270, 9360, 9450, 9630, 9660, 9870, 9900, 9990, 10080, 10260, 10290, 10500, 10530, 10620, 10710

Offset: 1

William Rex Marshall, Nov 20 2009

nonn

Every even number >= 3706141025766237065507279802221127212928 is the sum of two odd abundant numbers. The largest even number which does not appear in this sequence is unknown.

			945 is the smallest odd abundant number, so 945 + 945 = 1890 is the first term in the sequence.

Donovan Johnson, Table of n, a(n) for n = 1..1000

Cf. A005231, A048260.

mx=66240; x=vector(mx); k=144; v=vector(k); c=0; forstep(i=945, mx-1, 2, if(sigma(i)-2*i>0, c++; v[c]=i)); for(i=1, k, for(j=i, k, s=v[i]+v[j]; if(s<=mx, x[s]=1, next(2)))); c=0; forstep(n=1890, mx, 2, if(x[n]==1, c++; write("b168226.txt", c " " n))) /* Donovan Johnson, Jan 03 2013 */

A270660 Numbers in the range of the sum of abundant divisors function.

Original entry on oeis.org

12, 18, 20, 24, 30, 32, 36, 38, 40, 42, 44, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 180

Offset: 1

Timothy L. Tiffin, Jul 12 2016

nonn

Possible values for the sum of abundant divisors of the positive integers, written in ascending order.
Distinct nonzero values found in A187795.
The smallest odd integer in this sequence is 945, and the first run of three consecutive integers is 944, 945, 946.
This sequence contains every even integer greater than 46 and every odd integer greater than 20161.

Sin Hitotumatu, On the Limit for the Representation by the Sum of Two Abundant Numbers, Publications of the Research Institute for Mathematical Sciences of Kyoto University, 8 (1972/1973), 111-116.

Cf. A048242, supersequence of A005101 and A048260, A187795.

A271113 Numbers not in the range of the sum of abundant divisors function.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 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, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139

Offset: 1

Timothy L. Tiffin, Jul 13 2016

Numbers which do not appear in A187795 or in A270660; that is, there is no integer N whose sum of abundant divisors is equal to a(n) for any n.
This is a finite sequence that contains every odd positive integer less than 945, twelve even integers with 46 being the largest, and has the prime number 20161 as its last term.
A048242 contains the first three primitive abundant numbers: 12, 18, 20.

Sin Hitotumatu, On the Limit for the Representation by the Sum of Two Abundant Numbers, Publications of the Research Institute for Mathematical Sciences of Kyoto University, 8 (1972/1973), 111-116.

Cf. A005101, subsequence of A048242 and A263837, A048260, A187795, A270660 (complement).

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

PARI

A168226 Even numbers which are the sum of two odd abundant numbers.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

A270660 Numbers in the range of the sum of abundant divisors function.

Views

Author

Keywords

Comments

References

Crossrefs

A271113 Numbers not in the range of the sum of abundant divisors function.

Views

Author

Keywords

Comments

Links

Crossrefs