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A291882
a(n) is the least number k such that sigma(k+n) = Sum_{j=1..i} sigma(d_j), where d_j are the divisors of k.
1
1, 2, 10, 1183, 4514, 1179, 38, 3325, 9, 126855, 290, 261, 18, 6, 1930, 104771947, 344, 58, 326, 117, 270754, 13875, 32, 45, 32, 74, 70, 38, 18, 21200761175, 206, 1179, 86, 16, 56, 357, 85, 18, 124, 39948225, 361, 171, 1118, 63, 122, 38, 30, 239267, 482, 1367247
OFFSET
0,2
COMMENTS
a(123) > 10^11. - Giovanni Resta, Sep 15 2017
EXAMPLE
Divisors of 1183 are 1, 7, 13, 91, 169 and 1183: sigma(1) + sigma(7) + sigma(13) + sigma(91) + sigma(169) + sigma(1183)= 1 + 8 + 14 + 112 + 183 + 1464 = 1782 = sigma(1183+3) and 1183 is the least number to have this property.
MAPLE
with(numtheory): P:=proc(q) local a, b, j, k, n; for n from 0 to q do for k from 1 to q do
a:=divisors(k); b:=add(sigma(a[j]), j=1..nops(a));
if sigma(k+n)=b then print(k); break; fi; od; od; end: P(10^6);
PROG
(PARI) a(n) = my(k = 1); while(sigma(k+n) != sumdiv(k, d, sigma(d)), k++); k; \\ Michel Marcus, Sep 19 2017
CROSSREFS
Sequence in context: A008559 A245728 A171485 * A215650 A057015 A059732
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Sep 05 2017
EXTENSIONS
a(15), a(29), a(39), a(75), a(84), a(89), a(111) from Giovanni Resta, Sep 15 2017
STATUS
approved