

A269524


a(1) = 1, a(n) counts m < n for which a(m) has at most as many divisors as n.


1



1, 1, 2, 3, 4, 5, 5, 7, 8, 9, 7, 11, 9, 13, 14, 15, 10, 17, 11, 19, 20, 20, 13, 23, 18, 22, 23, 27, 16, 29, 17, 31, 28, 28, 28, 35, 19, 30, 30, 39, 20, 41, 21, 41, 42, 34, 22, 47, 26, 46, 39, 48, 23, 52, 41, 54, 42, 42, 25, 59, 26, 45, 55, 56
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OFFSET

1,3


LINKS

Peter Kagey, Table of n, a(n) for n = 1..10000


EXAMPLE

a(1) = 1;
a(2) = 1 because a(1) has as many or fewer divisors as 2;
a(3) = 2 because a(1) and a(2) have as many or fewer divisors as 3;
a(4) = 3 because a(1), a(2), and a(3) have as many or fewer divisors than 4;
(...)
a(7) = 5 because a(1), a(2), a(3), a(4), and a(6) have as many or fewer divisors as 7.


MATHEMATICA

a = {1}; Do[d = DivisorSigma[0, n]; AppendTo[a, Count[a, k_ /; DivisorSigma[0, k] <= d]], {n, 2, 64}]; a (* Michael De Vlieger, Feb 29 2016 *)


PROG

(Java)
int[] terms = new int[100];
terms[0] = 1;
for (int i = 1; i < 100; i++) {
int count = 0;
for (int j = 0; j < i; j++) {
if (divisors(terms[j]) <= divisors(i+1)) {
count = count + 1;
}
}
terms[i] = count;
}
(PARI) lista(nn) = {va = vector(nn); print1(va[1] = 1, ", "); for (n=2, nn, va[n] = sum(k=1, n1, numdiv(va[k]) <= numdiv(n)); print1(va[n], ", "); ); } \\ Michel Marcus, Feb 29 2016


CROSSREFS

Cf. A032741.
Sequence in context: A082081 A008475 A222416 * A161656 A306328 A225090
Adjacent sequences: A269521 A269522 A269523 * A269525 A269526 A269527


KEYWORD

easy,nonn


AUTHOR

Alec Jones, Feb 28 2016


STATUS

approved



