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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
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
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. A262508 (positions of ones).
Cf. A263260 (partial sums).
Sequence in context: A267808 A239852 A263279 * A151679 A077664 A329402
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 25 2015
STATUS
approved