A246851 a(n) = smallest number k such that sigma(k+n) - sigma(k) = k + n, or -1 if no solution exists.

1, 1, 7, 1, 3577, 1, 25, 8, 13, 1, 403668223, 1, 833, 262, 19, 1, 27, 1, 793, 5, 45, 1, 1795, 66, 8, 9, 31, 1, 2005, 1, 309, 32, 261, 4238, 22490141, 1, 21, 40, 43, 1, 399, 1, 1897, 262, 193, 1, 27, 1252907952, 711, 49, 1158765, 1, 271259, 27, 129, 20518072

Offset

1,3

Comments

a(p-1) = 1 for any prime p.

a(11) > 11*10^8. - Derek Orr, Sep 05 2014

a(35) > 88*10^7. - Derek Orr, Sep 05 2014

a(185), a(385) and a(869) > 10^11. - Hiroaki Yamanouchi, Sep 11 2014

Links

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..184

Example

Sequence of numbers k < 10^7  such that sigma(k+n) - sigma(k) = k + n for 1 <= n <= 10:
n = 1: 1, 5, 8585, 16119, ... (A067816).
n = 2: 1, 2, 22, 14926, 31048, 69106, 246262, 5860168, ... (A246852).
n = 3: 7, 6285, 4693485, ... (A246853).
n = 4: 1, 4, 26, 122, 146, 458, 746, 3746, 47612, ... (A246854).
n = 5: 3577, 14773, 2843579, ... (A246855).
n = 6: 1, 3, 114, 116058, 340014, ...
n = 7: 25, 65017, ...
n = 8: 8, 34, 76, 13474, 19042, ...
n = 9: 13, 1743, 1773, 4323, 53175, 109035, 138535, ...
n = 10: 1, 20, 1958, 35150, 49010, 246686, 1030046, 1240694, ...

Prog

(Magma) A246851:=func<n|exists(r){m: m in[1..1000000] | SumOfDivisors(m+n)-SumOfDivisors(m)eq m+n}select r else-1>; [A246851(n): n in[1..100]]

Crossrefs

Cf. A000203, A067816, A246852, A246853, A246854, A246855.

Sequence in context: A245329 A309171 A296791 * A258763 A258753 A248363

Adjacent sequences: A246848 A246849 A246850 * A246852 A246853 A246854

Keyword

sign

Author

Jaroslav Krizek, Sep 05 2014

Extensions

a(11)-a(56) from Hiroaki Yamanouchi, Sep 11 2014

Status

approved