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.
6, 20, 28, 45, 63, 70, 88, 99, 104, 105, 110, 117, 130, 154, 165, 170, 182, 195, 231, 238, 255, 266, 272, 273, 285, 286, 304, 322, 345, 357, 368, 374, 385, 399, 418, 429, 455, 459, 464, 475, 483, 494, 496, 506, 513, 561, 595, 598, 609, 621, 627, 646, 651, 663
Offset: 1
Keywords
Examples
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. 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.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A119357.
Programs
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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;} isA119357(n) = {my(vsd = sums(n)); #Set(vsd) < #vsd;} isprmi(n, v) = {for (k=1, #v, if (! (n % v[k]), return (0););); return (1);} 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
Comments