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A263093 Numbers whose squares are in A045765. 5
5, 6, 7, 8, 10, 14, 16, 18, 20, 22, 26, 27, 28, 34, 35, 37, 46, 47, 50, 54, 56, 58, 59, 60, 62, 67, 73, 78, 82, 85, 89, 90, 94, 95, 98, 100, 103, 104, 106, 110, 114, 116, 118, 122, 124, 125, 126, 127, 128, 130, 135, 140, 141, 142, 148, 150, 155, 158, 161, 164, 170, 172, 174, 177, 178, 182, 184, 188, 190, 199, 202, 205, 207 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers n such that there is no such k for which k - d(k) = n^2, where d(k) is the number of divisors of k (A000005).

Numbers n for which A060990(n^2) = A263087(n) = 0.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..12443

A. Karttunen, Ratio a(n)/A263092(n) drawn with the help of OEIS Plot2-utility

FORMULA

a(n) = A000196(A263095(n)).

PROG

(PARI)

\\ Compute A263093 and A263095 at the same time:

A060990(n) = { my(k = n + 1440, s=0); while(k > n, if(((k-numdiv(k)) == n), s++); k--; ); s}; \\ Hard limit 1440 is good for at least up to A002182(67) = 1102701600 as A002183(67) = 1440.

n = 1; k = 0; while((n^2)<1102701600, if((0 == A060990(n*n)), k++; write("b263093.txt", k, " ", n); write("b263095.txt", k, " ", (n*n)); ); n++; if(!(n%8192), print1(n, ", k=", k, ", ")); );

(Scheme, with Antti Karttunen's IntSeq-library)

(define A263093 (MATCHING-POS 1 1 (lambda (n) (zero? (A060990 (* n n))))))

(define A263093 (ZERO-POS 1 0 A263087))

CROSSREFS

Cf. A000005, A000196, A045765, A049820, A060990, A263098.

Complement: A263092.

Positions of zeros in A263087 and positions of ones in A263088.

Cf. A263095 (the squares of these numbers).

Sequence in context: A037361 A202014 A319266 * A115839 A200259 A339746

Adjacent sequences:  A263090 A263091 A263092 * A263094 A263095 A263096

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 11 2015

STATUS

approved

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Last modified November 30 21:20 EST 2021. Contains 349426 sequences. (Running on oeis4.)