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A246851 a(n) = smallest number k such that sigma(k+n) - sigma(k) = k + n, or -1 if no solution exists. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 11 07:36 EST 2019. Contains 329914 sequences. (Running on oeis4.)