cp's OEIS Frontend

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.

%I A119425 #12 Jan 11 2023 06:39:52
%S A119425 6,20,28,45,63,70,88,99,104,105,110,117,130,154,165,170,182,195,231,
%T A119425 238,255,266,272,273,285,286,304,322,345,357,368,374,385,399,418,429,
%U A119425 455,459,464,475,483,494,496,506,513,561,595,598,609,621,627,646,651,663
%N 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.
%C A119425 The sequence A119357 is closed under multiplication by positive integers and the primitive terms are those that are not multiples of other terms.
%H A119425 Amiram Eldar, <a href="/A119425/b119425.txt">Table of n, a(n) for n = 1..10000</a>
%e A119425 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 A119425 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 A119425 (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 A119425 isA119357(n) = {my(vsd = sums(n)); #Set(vsd) < #vsd;}
%o A119425 isprmi(n, v) = {for (k=1, #v, if (! (n % v[k]), return (0););); return (1);}
%o A119425 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 A119425 Cf. A119357.
%K A119425 nonn
%O A119425 1,1
%A A119425 _Emeric Deutsch_, May 20 2006