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A262507 a(n) = number of times n occurs in A155043. 15
1, 2, 3, 5, 4, 5, 6, 4, 4, 4, 8, 4, 4, 5, 8, 7, 7, 7, 7, 8, 5, 6, 6, 8, 10, 7, 8, 7, 7, 5, 5, 6, 6, 8, 6, 7, 7, 7, 4, 5, 5, 6, 6, 8, 7, 5, 5, 6, 7, 11, 5, 4, 5, 8, 12, 7, 9, 5, 8, 8, 9, 10, 14, 11, 12, 11, 9, 11, 13, 12, 12, 11, 11, 11, 12, 12, 10, 9, 9, 9, 8, 6, 10, 9, 10, 8, 7, 7, 8, 11, 10, 10, 12, 9, 7, 6, 5, 5, 5, 5, 4, 7, 8, 6, 7, 9, 7, 5, 11, 13, 13, 8, 10, 12, 13, 10, 12, 16, 9, 8, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Records are: 1, 2, 3, 5, 6, 8, 10, 11, 12, 14, 16, 17, 19, 21, 22, 24, 25, 26, 27, 31, 35, 39, 44, ... and they occur at positions: 0, 1, 2, 3, 6, 10, 24, 49, 54, 62, 117, 236, 445, 484, 892, 893, 1022, 1784, 1911, 1912, 1913, 20600, 50822, ...

a(n) gives the length of each row of irregular table A263265.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..110880

FORMULA

a(n) = Sum_{k=n..A262502(2+n)} [A155043(k) == n]. (Here [...] denotes the Iverson bracket, resulting 1 when A155043(k) is n and 0 otherwise.)

Other identities. For all n >= 0:

a(n) = A263279(n) + A263280(n).

PROG

(PARI)

allocatemem(123456789);

uplim = 2162160; \\ = A002182(41).

v155043 = vector(uplim);

v155043[1] = 1; v155043[2] = 1;

for(i=3, uplim, v155043[i] = 1 + v155043[i-numdiv(i)]);

uplim2 = 110880; \\ = A002182(30).

v262507 = vector(uplim2);

for(i=1, uplim, if(v155043[i] <= uplim2, v262507[v155043[i]]++));

A262507 = n -> if(!n, 1, v262507[n]);

for(n=0, uplim2, write("b262507.txt", n, " ", A262507(n)));

(Scheme)

(define (A262507 n) (add (lambda (k) (if (= (A155043 k) n) 1 0)) n (A262502 (+ 2 n))))

;; Auxiliary function add implements sum_{i=lowlim..uplim} intfun(i)

(define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (1+ i) (+ res (intfun i)))))))

CROSSREFS

Cf. A000005, A060990, A155043, A262502, A262505, A263265, A263270, A263279, A263280.

Cf. A261089, A262503.

Cf. A262508 (positions of ones).

Cf. A263260 (partial sums).

Sequence in context: A267808 A239852 A263279 * A151679 A077664 A329402

Adjacent sequences:  A262504 A262505 A262506 * A262508 A262509 A262510

KEYWORD

nonn

AUTHOR

Antti Karttunen, Sep 25 2015

STATUS

approved

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Last modified August 16 20:22 EDT 2022. Contains 356169 sequences. (Running on oeis4.)