

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
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OFFSET

1,3


COMMENTS

a(p1) = 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<nexists(r){m: m in[1..1000000]  SumOfDivisors(m+n)SumOfDivisors(m)eq m+n}select r else1>; [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



