A302110 - OEIS

A302110

Let d be the list of A000005(n) = tau(n) divisors of n. Then a(n) is the largest k such that Sum_{i=1..#d-k} d_i > n.

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1

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OFFSET

1,24

COMMENTS

Records (0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, ...) occur at 1, 6, 24, 120, 240, 720, 1260, 2520, 5040, 15120, 27720, 55440, ... - Antti Karttunen, Apr 02 2018

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

FORMULA

a(n) = A000005(n) - A125747(n).

a(n) > 0 if and only if n is in A023196.

PROG

(PARI)

A125747(n) = { my(k=0, s=0); fordiv(n, d, k++; s += d; if(s>=n, return(k))); };

A302110(n) = (numdiv(n) - A125747(n)); \\ Antti Karttunen, Apr 02 2018

CROSSREFS

Cf. A000005, A023196, A125746, A125747, A300826.

Sequence in context: A294890 A325562 A176917 * A085983 A285701 A088183

Adjacent sequences: A302107 A302108 A302109 * A302111 A302112 A302113

KEYWORD

nonn,easy

AUTHOR

David A. Corneth, Apr 01 2018

STATUS

approved