

A086986


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


1



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, 65, 66, 67, 68, 69, 70, 71, 73, 75, 76, 77, 78, 81, 82, 83, 84, 85, 86, 87, 89
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OFFSET

1,1


COMMENTS

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


LINKS



EXAMPLE

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


PROG

(PARI) { s=vector(1000); sc=0; for (k=1, 10, for (i=1, 100, s[sc++ ]=sum(j=0, k, sigma(i+j)))); s=vecsort(s); s } for (i=2, 100, for (j=1, 1000, if (sigma(i)==s[j], print1(i", "); break)))


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



