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A034094 (-1)sigma perfect numbers: (-1)sigma(a) = m*a for some integer m, where if a = Product p(i)^r(i) then (-1)sigma(a) = Product (-1+Sum p(i)^s(i), s(i)=1 to r(i)). 3
1, 20, 312, 9744, 29280, 53352, 1666224, 5006880, 106798080, 980733600, 133301760, 9099742080, 22794600960, 1556055895680, 3577201689600, 4464942451200, 380428773854896765462278360268800000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The indices of some terms are 1, so these numbers are fixed points of (-1)sigma where (-1)sigma is A049060.

LINKS

Table of n, a(n) for n=1..17.

EXAMPLE

Factorizations 2^2*5, 2^3*3*13, 2^4*3*7*29, 2^5*3*5*61, 2^3*3^3*13*19, 2^4*3^3*7*19*29, 2^5*3^3*5*19*61, 2^10*3*5*17*409, 2^5*3^2*5^2*7*11*29*61, 2^9*3*5*17*1021, 2^7*3*5*11^2*13*23*131, 2^9*3^3*5*17*19*1021, 2^7*3^3*5*11^2*13*19*23*131, 2^10*3^2*5^2*7*11*17*29*409, 2^9*3^2*5^2*7*11*17*29*1021, 2^24*3^3*5^5*7^2*11*17*19*29*61*233*239*467*479*70051.

PROG

(PARI) msig(n) = {f = factor(n); for (i=1, #f~, f[i, 1] = (f[i, 1]^(f[i, 2]+1)-2*f[i, 1]+1)/(f[i, 1]-1); f[i, 2] = 1; ); factorback(f); }

isok(n) = denominator(msig(n)/n) == 1; \\ Michel Marcus, Jun 02 2016

CROSSREFS

Cf. A034095, A049060.

Sequence in context: A282372 A240799 A281931 * A011197 A054621 A111778

Adjacent sequences:  A034091 A034092 A034093 * A034095 A034096 A034097

KEYWORD

nonn,more

AUTHOR

Yasutoshi Kohmoto

EXTENSIONS

a(1)=1 prepended by Michel Marcus, Jun 02 2016

STATUS

approved

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Last modified January 16 03:55 EST 2019. Contains 319184 sequences. (Running on oeis4.)