login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A119425 Primitive terms of the sequence A119357, i.e., of the sequence of those values of n for which the number of distinct nonzero sums of distinct divisors of n is less than 2^tau(n) - 1. 1

%I

%S 6,20,28,45,63,70,88,99,104,105,110,117,130,154,165,170,182,195,231,

%T 238,255,266,272,273,285,286,304,322,345,357,368,374,385,399,418,429,

%U 455,459,464,475,483,494,496,506,513,561,595,598,609,621,627,646,651,663

%N Primitive terms of the sequence A119357, i.e., of the sequence of those values of n for which the number of distinct nonzero sums of distinct divisors of n is less than 2^tau(n) - 1.

%C The sequence A119357 is closed under multiplication by positive integers and the primitive terms are those that are not multiples of other terms.

%e 45 is in the sequence because (i) the divisors 1, 5, 9, 15 of 45 satisfy 15 = 1 + 5 + 9 (consequently the number of distinct nonzero sums of distinct divisors of 45 is less than 2^tau(45) - 1) and (ii) no proper divisor of 45 has this property.

%e The first terms of A119357 are 6, 12, 18, 20, 24, 28, 30, 36, 40, 42, 45, 48 and, consequently, the first terms of this sequence are 6, 20, 28, 45.

%o (PARI) sums(n) = {my (divs = divisors(n)); my (nbdivs = #divs); my (nb = 2^nbdivs-1); my (vsd = vector(nb)); for (i=1, nb, vb = padbin(i, nbdivs); vsd[i] = sum(j=1, nbdivs, divs[j]*vb[j]);); vsd;}

%o isA119357(n) = {my(vsd = sums(n)); #Set(vsd) < #vsd;}

%o isprmi(n, v) = {for (k=1, #v, if (! (n % v[k]), return (0););); return (1);}

%o lista(nn) = {my(vless = []); for (n=1, nn, if (isprmi(n, vless) && isA119357(n), vless = concat(vless, n); print1(n, ", ");););} \\ _Michel Marcus_, Jan 13 2014

%Y Cf. A119357.

%K nonn

%O 1,1

%A _Emeric Deutsch_, May 20 2006

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 23 08:40 EDT 2021. Contains 348211 sequences. (Running on oeis4.)