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

1,1

Comments

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

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

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.

Prog

(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

Crossrefs

Cf. A119357.

Sequence in context: A090502 A324649 A324643 * A342669 A006039 A180332

Adjacent sequences: A119422 A119423 A119424 * A119426 A119427 A119428

Keyword

nonn

Author

Emeric Deutsch, May 20 2006

Status

approved