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 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
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified September 28 06:05 EDT 2021. Contains 347703 sequences. (Running on oeis4.)