A086986 - OEIS

A086986

Numbers n such that sigma(n) can be represented as Sum_{i=0..k} sigma(m+i), with k>0.

3, 4, 7, 8, 9, 10, 12, 13, 16, 17, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 75, 76, 77, 78, 81, 82, 83, 84, 85, 86, 87, 89

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Is it true that every integer n ultimately has sigma(n) representable like this?

LINKS

Table of n, a(n) for n=1..72.

EXAMPLE

sigma(61) = 62 = sigma(13) + sigma(14) + sigma(15) = 14 + 24 + 24.

PROG

(PARI) isok(n)=my(m=sigma(n)); for(k=1, m\2, my(s=sigma(k), j=k); while(s<m, j++; s+=sigma(j); if(s==m, return(1)))); 0 \\ Andrew Howroyd, Sep 13 2024

CROSSREFS

Cf. A086987 gives values of sigma, A000203.

Sequence in context: A097044 A198330 A232779 * A346126 A057811 A284489

Adjacent sequences: A086983 A086984 A086985 * A086987 A086988 A086989

KEYWORD

nonn

AUTHOR

Jon Perry, Jul 27 2003

EXTENSIONS

Missing a(52)=64 inserted by Andrew Howroyd, Sep 13 2024

STATUS

approved