A271606 - OEIS

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A271606

Number of numbers k such that sigma_e(k) = n for some e > 0.

1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 1, 1, 0, 1, 2, 0, 1, 1, 0, 0, 3, 0, 1, 0, 2, 0, 1, 2, 2, 1, 0, 0, 1, 0, 1, 1, 1, 0, 3, 0, 1, 0, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0, 2, 1, 0, 0, 3, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 5, 1, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 3, 1, 0, 0, 0, 0, 3, 2, 0, 1, 0, 0, 4, 0, 2, 0, 0

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OFFSET

1,12

COMMENTS

We can't just define this as number of pairs k, e with e > 0 that have sigma_e(k) = n, because sigma_e(1) = 1 for all e.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

a(28) = 2 because 28 = sigma_1(12) = 1+2+3+4+6+12 and also 28 = sigma_3(3) = 1^3+3^3.

PROG

(PARI) alist(n)=my(r=vector(n), s); r[1]=1; for(k=2, n, e=1; while((s=sigma(k, e))<=n, r[s]++; e++)); r

CROSSREFS