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

Author

Paolo P. Lava, Sep 05 2017

Keywords

• nonn

Comments

a(123) > 10^11. - Giovanni Resta, Sep 15 2017

Examples

			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.
		

Links

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

Crossrefs

Cf. A000203, A066218.

Programs

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);

PARI

a(n) = my(k = 1); while(sigma(k+n) != sumdiv(k, d, sigma(d)), k++); k; \\ Michel Marcus, Sep 19 2017

Extensions

a(15), a(29), a(39), a(75), a(84), a(89), a(111) from Giovanni Resta, Sep 15 2017