login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A298156 Composite numbers n of which the sum of prime divisors of n (with repetition) equals the concatenation of two integers k and k + 1. 1
35, 42, 50, 60, 64, 72, 76, 81, 86, 93, 136, 145, 153, 159, 164, 174, 253, 273, 289, 325, 365, 385, 390, 416, 438, 462, 468, 488, 494, 497, 549, 550, 555, 559, 592, 644, 658, 660, 664, 666, 686, 703, 704, 710, 737, 747, 792, 836, 852, 884, 885, 891, 920, 940, 944, 946, 980 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Composite numbers n, of which A001414(n) (sum of prime divisors of n with repetition, sopfr(n)) is in sequence A001704 (numbers m which are the concatenation of k and k+1).

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

K. Alladi and P. Erdős, On an additive arithmetic function, Pacific J. Math., Volume 71, Number 2 (1977), 275-294.

Eric Weisstein's World of Mathematics, Sum of Prime Factors

FORMULA

sopfr(n) = k||k+1 when n is not prime and k is a positive integer.

EXAMPLE

35 = 5*7, sopfr(35) = 5+7 = 12, 12 =k||k+1 when k = 1.

MATHEMATICA

Select[Range[10^3], And[CompositeQ@ #, Subtract @@ Map[FromDigits, TakeDrop[#, Floor[Length[#]/2]]] == -1 &@ IntegerDigits@ Total[Flatten@ Map[ConstantArray[#1, #2] & @@ # &, FactorInteger[#]]]] &] (* Michael De Vlieger, Jan 14 2018 *)

PROG

(PARI) is(n)=my(f = factor(n), sopfr = sum(i = 1, #f~, f[i, 1] * f[i, 2]); d = digits(sopfr), v); if((#d) % 2 == 0, v = vector(#d / 2); v[#v] = -1; return(vector(#d / 2, j, d[j]) - vector(#d / 2, #d / 2 + j, d[j]) == v), return(d == concat(digits(10^(#d \ 2) - 1), digits(10^(#d \ 2))))) \\ David A. Corneth, Jan 13 2018

(PARI) sopfr(n, f=factor(n))=sum(i=1, #f~, f[i, 1]*f[i, 2])

has(n)=my(d=digits(n), k=#d); digits(fromdigits(d[1..k\2])+1) == d[k\2+1..k]

list(lim)=my(v=List()); forfactored(n=35, lim\1, if(n[2][, 2]!=[1]~ && has(sopfr(0, n[2])), listput(v, n[1]))); Vec(v) \\ Charles R Greathouse IV, Jan 15 2018

CROSSREFS

Cf. A001414 (sum of prime divisors of n with repetition, sopfr(n)).

Cf. A001704 (numbers which are the concatenation of k and k+1).

Sequence in context: A217007 A141741 A122755 * A167326 A141638 A033857

Adjacent sequences: A298153 A298154 A298155 * A298157 A298158 A298159

KEYWORD

base,nonn

AUTHOR

Daniel Blaine McBride, Jan 13 2018

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 15:01 EST 2022. Contains 358667 sequences. (Running on oeis4.)