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, 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

Links

Table of n, a(n) for n=0..49.

Paolo P. Lava, Terms from a(1) to a(300) ('?' for unknown values)

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

Cf. A000203, A066218.

Sequence in context: A008559 A245728 A171485 * A215650 A057015 A059732

Adjacent sequences: A291879 A291880 A291881 * A291883 A291884 A291885

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